Zabavnikova, T. A.; Kadashevich, Yu. I.; Pomytkin, S. P.
2018-05-01
A geometric non-linear endochronic theory of inelasticity in tensor parametric form is considered. In the framework of this theory, the creep strains are modelled. The effect of various schemes of applying stresses and changing of material properties on the development of creep strains is studied. The constitutive equations of the model are represented by non-linear systems of ordinary differential equations which are solved in MATLAB environment by implicit difference method. Presented results demonstrate a good qualitative agreement of theoretical data and experimental observations including the description of the tertiary creep and pre-fracture of materials.
A phenomenological theory of transient creep
International Nuclear Information System (INIS)
Ajaja, O.; Ardell, A.J.
1979-01-01
A new creep theory is proposed which takes into account the strain generated during the annihilation of dislocations. This contribution is found to be very significant when recovery is appreciable, and is mainly responsible for the decreasing creep rate associated with the normal primary creep of class II materials. The theory provides excellent semiquantitative rationalization for the types of creep curves presented in the preceding paper. In particular, the theory predicts a change in the shape of the primary creep curve from normal to inverted as recovery becomes less important, i.e. as the applied stress and/or temperature decrease(s). It also predicts a minimum creep rate under certain circumstances, hence pseudo-tertiary behaviour. These different types of creep curves are predicted even though the net dislocation density decreases monotonically with time in all cases. Qualitative rationalization is presented for the inverted transient which always follows a stress drop in class II materials, as well as for the inverted primary and sigmoidal creep behaviour of class I solid solutions. (author)
Yankovskii, A. P.
2015-05-01
An indirect verification of a structural model describing the creep of a composite medium reinforced by honeycombs and made of nonlinear hereditary phase materials obeying the Rabotnov theory of creep is presented. It is shown that the structural model proposed is trustworthy and can be used in practical calculations. For different kinds of loading, creep curves for a honeycomb core made of a D16T aluminum alloy are calculated.
Finite element analysis of nonlinear creeping flows
International Nuclear Information System (INIS)
Loula, A.F.D.; Guerreiro, J.N.C.
1988-12-01
Steady-state creep problems with monotone constitutive laws are studied. Finite element approximations are constructed based on mixed Petrov-Galerkin formulations for constrained problems. Stability, convergence and a priori error estimates are proved for equal-order discontinuous stress and continuous velocity interpolations. Numerical results are presented confirming the rates of convergence predicted in the analysis and the good performance of this formulation. (author) [pt
Thermal effects, creep and nonlinear responde of concrete reactor vessels
International Nuclear Information System (INIS)
Bazant, Z.P.
1978-01-01
A new mathematical model for prediction of pore pressure and moisture transfer in concrete heated well beyond 100 0 C is outlined. The salient features of the model are:(1) the hypothesis taht the pore space available to capillary water grows with increasing temperature as well as increasing pressure in excess of saturation pressure, and (2) the hypothesis that moisture permeability increases by two orders of magnitude when passing 100 0 C. Permaability below 100 0 C is controlled by migration of adsorbed water through gel-pore sized necks on passages through the material; these necks are lost above 100 0 C and viscosity then governs. The driving force of moisture transfer may be considered as the gradient of pore pressure, which is defined as pressure of vapor rather than liquid water if concrete is not saturated. Thermodynamic properties of water may be used to determine sorption isotherms in saturated concrete. The theory is the necessary first step in rationally predicting thermal stresses and deformations, and assessing the danger of explosive spalling. However, analysis of creep and nonlinear triaxial behavior is also needed for this purpose. A brief review of recent achievements in these subjects is also given. (Author)
Creep theories compared by means of high sensitivity tensile creep data
International Nuclear Information System (INIS)
Salim, A.
1987-01-01
Commonly used creep theories include time-hardening, strain-hardening and Rabotnov's modified strain-hardening. In the paper they are examined by using high sensitivity tensile creep data produced on 1% CrMoV steel at a temperatue of 565 0 C. A special creep machine designed and developed by the author is briefly described and is compared with other existing machines. Tensile creep data reported cover a stress range of 100-260 MN m -2 ; four variable-creep tests each in duplicate are also reported. Test durations are limited to 3000 h, or failure, whichever occurs earlier. The strain-hardening theory and Rabotnov's modified strain-hardening theory are found to give good prediction of creep strain under variable stress conditions. The time-hardening theory shows a relatively poor agreement and considerably underestimates the accumulated inelastic strain under increasing stress condition. This discrepancy increases with the increased stress rate. The theories failed to predict the variable stress results towards the later part of the test where tertiary effects were significant. The use of creep equations which could account for creep strain at higher stress levels seems to improve the situation considerably. Under conditions of variable stress, it is suggested that a theory based on continuous damage mechanics concepts might give a better prediction. (author)
Nonlinear Subincremental Method for Determination of Elastic-Plastic-Creep Behaviour
DEFF Research Database (Denmark)
Ottosen, N. Saabye; Gunneskov, O.
1985-01-01
to general elastic-plastic-creep behaviour including problems with a highly nonlinear total strain path caused by the occurrence of creep hardening. This nonlinear method degenerates to the linear approach for elastic-plastic behaviour and when secondary creep is present. It is also linear during step......The frequently used subincremental method has so far been used on a linear interpolation of the total strain path within each main step. This method has proven successful when elastic-plastic behaviour and secondary creep is involved. The authors propose a nonlinear subincremental method applicable...
Nonlinear optimal control theory
Berkovitz, Leonard David
2012-01-01
Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also dis
Recovery from nonlinear creep provides a window into physics of polymer glasses
Caruthers, James; Medvedev, Grigori
Creep under constant applied stress is one of the most basic mechanical experiments, where it exhibits extremely rich relaxation behavior for polymer glasses. As many as five distinct stages of nonlinear creep are observed, where the rate of creep dramatically slows down, accelerates and then slows down again. Modeling efforts to-date has primarily focused on predicting the intricacies of the nonlinear creep curve. We argue that as much attention should be paid to the creep recovery response, when the stress is removed. The experimental creep recovery curve is smooth, where the rate of recovery is initially quite rapid and then progressively decreases. In contrast, the majority of the traditional constitutive models predict recovery curves that are much too abrupt. A recently developed stochastic constitutive model that takes into account the dynamic heterogeneity of glasses produces a smooth creep recovery response that is consistent with experiment.
Magnetic flux creep in HTSC and Anderson-Kim theory
International Nuclear Information System (INIS)
Lykov, A.N.
2014-01-01
The theoretical and experimental data on flux creep in high-temperature superconductors (HTSC) were analyzed in the review paper. On the one hand, the main attention is paid to the most striking experimental results which have had a significant influence on the investigations of flux creep in HTSC. On the other hand, the analysis of theoretical studies is concentrated on the works, which explain the features of flux creep on the basis of the Anderson-Kim (AK) theory modifications, and received previously unsufficient attention. However, it turned out that the modified AK theory could explain a lot of features of flux creep in HTSC: the scaling behaviour of current-voltage curves of HTSC, the finite rate of flux creep at ultra low temperatures, the logarithmic dependence of effective pinning potential as a function of transport current and its decrease with temperature. The harmonic potential field which is used in this approach makes it possible to solve accurately the both problems: viscous vortex motion and flux creep in this field. Moreover the distribution of pinning potential and the interaction of vortices with each other are taken into account in the approach. Thus, the modification of the AK theory consists, essentially, in its detailed elaboration and approaching to real situations in superconductors
International Nuclear Information System (INIS)
Berthollet, A.
2003-10-01
Concrete structures are examined during their lifetime and often present important cracking states, which can progress with time and lead to change the structural behavior. The civil engineering works that the main function corresponds to protection's wall are very sensitive to this damage and its evolution. The growth of the time - dependent cracks represents an aging pathology linked with interaction between creep mechanism and the non-linear behavior of the material. In this thesis, a modeling for these mechanisms and their coupling are proposed. It based on creep strains analysis under different load levels, on the influence of the rate effect to the mechanical behavior. A stress limit is put on prominent manner, where beyond it, the creep - cracking interaction becomes important with the introduction of the ultimate tertiary creep kinetic. This level of strength is identified for infinitely slow loading rates and is also called intrinsic strength. It defines the limit on this side the viscous behavior of the cement paste limits the irreversibility processes as cracking. Thus, a constitutive law of viscoelastic - viscoplastic behavior with a high coupling between the cracking mechanism and the creep strains is proposed. The developments of the model are built on DUVAUT - LIONS approach integrated a generalized MAXWELL chain model. For one part, the viscoelastic behavior translates the creep mechanism under low stresses. For a second part, it associated with the viscoplastic behavior, which allows introducing both creep effect under high stresses and rate effect acting on micro-cracked zones. The cracking mechanism is described throughout a plasticity theory with multi-criteria, which induce a property of anisotropy for hardening. Qualitatively, ails of the creep kinetics are reproduced. An additional validation is based on experimental tests in compression, traction and flexion where the main parameters of the modeling are detailed. Thus, we can conclude on the
Microprestress - solidification theory for aging and drying creep of concrete
DEFF Research Database (Denmark)
Bazant, Zdenek P.; Hauggaard-Nielsen, Anders Boe; Baweja, Sandeep
1996-01-01
A new physical theory for the effects of long-term aging and drying on concrete creep is proposed. The previously proposed solidification theory, in which aging is explained and modeled by the volume growth (into the pores of hardened Portland cement paste) of a nonaging viscoelastic constituent...... external load or the macroscopic continuum deformation of concrete can cause only very small changes of the microprestress, such that the response to load is determined by tangential linearization. Relaxation of the microprestress causes the tangential viscosity to increase, which reduces long-term creep....... A decrease of relative humidity in the pores causes (due to changes of capillary tension, surface tension and disjoining pressure) a large increase in the microprestress, which in turn reduces tangential viscosity and thus increases the creep rate. This explains the drying effect (Pickett effect...
Creep Damage Evaluation of Titanium Alloy Using Nonlinear Ultrasonic Lamb Waves
International Nuclear Information System (INIS)
Xiang Yan-Xun; Xuan Fu-Zhen; Deng Ming-Xi; Chen Hu; Chen Ding-Yue
2012-01-01
The creep damage in high temperature resistant titanium alloys Ti60 is measured using the nonlinear effect of an ultrasonic Lamb wave. The results show that the normalised acoustic nonlinearity of a Lamb wave exhibits a variation of the 'increase-decrease' tendency as a function of the creep damage. The influence of microstructure evolution on the nonlinear Lamb wave propagation has been analyzed based on metallographic studies, which reveal that the normalised acoustic nonlinearity increases due to a rising of the precipitation volume fraction and the dislocation density in the early stage, and it decreases as a combined result of dislocation change and micro-void initiation in the material. The nonlinear Lamb wave exhibits the potential for the assessment of the remaining creep life in metals
Nonlinear theory of elastic shells
International Nuclear Information System (INIS)
Costa Junior, J.A.
1979-08-01
Nonlinear theory of elastic shells is developed which incorporates both geometric and physical nonlinearities and which does not make use of the well known Love-Kirchhoff hypothesis. The resulting equations are formulated in tensorial notation and are reduced to the ones of common use when simplifying assumptions encountered in the especific litterature are taken. (Author) [pt
Non-linearities in tensile creep of concrete at early age
DEFF Research Database (Denmark)
Hauggaard-Nielsen, Anders Boe; Damkilde, Lars
1997-01-01
A meterial model for creep is proposed which takes into consideration some of the couplings in early age concrete. The model is in incremental form and reflect the hydration process where new layers of cement gel are formed in a stress free state. In the present context attention is on non......-linear creep at high stress levels. The parameteres in the model develop in time as a result of hydration. The creep model has been used to analyse the tensile experiments at different stress levels carried out in the HETEK project. The tests were made on dogbone shaped specimen and the test procedure...
Nonlinear classical theory of electromagnetism
International Nuclear Information System (INIS)
Pisello, D.
1977-01-01
A topological theory of electric charge is given. Einstein's criteria for the completion of classical electromagnetic theory are summarized and their relation to quantum theory and the principle of complementarity is indicated. The inhibiting effect that this principle has had on the development of physical thought is discussed. Developments in the theory of functions on nonlinear spaces provide the conceptual framework required for the completion of electromagnetism. The theory is based on an underlying field which is a continuous mapping of space-time into points on the two-sphere. (author)
Yankovskii, A. P.
2017-09-01
The creep of homogenous and hybrid composite beams of an irregular laminar fibrous structure is investigated. The beams consist of thin walls and flanges (load-carrying layers). The walls may be reinforced longitudinally or crosswise in the plane, and the load-carrying layers are reinforced in the longitudinal direction. The mechanical behavior of phase materials is described by the Rabotnov nonlinear hereditary theory of creep taking into account their possible different resistance to tension and compression. On the basis of hypotheses of the Timoshenko theory, with using the method of time steps, a problem is formulated for the inelastic bending deformation of such beams with account of the weakened resistance of their walls to the transverse shear. It is shown that, at discrete instants of time, the mechanical behavior of such structures can formally be described by the governing relations for composite beams made of nonlinear elastic anisotropic materials with a known initial stress state. The method of successive iterations, similar to the method of variable parameters of elasticity, is used to linearize the boundary-value problem at each instant of time. The bending deformation is investigated for homogeneous and reinforced cantilever and simply supported beams in creep under the action of a uniformly distributed transverse load. The cross sections of the beams considered are I-shaped. It is found that the use of the classical theory for such beams leads to the prediction of indefensibly underestimated flexibility, especially in long-term loading. It is shown that, in beams with reinforced load-carrying layers, the creep mainly develops due to the shear strains of walls. It is found that, in short- and long-term loadings of composite beams, the reinforcement structures rational by the criterion of minimum flexibility are different.
A nonlinear finite element model of a piezoelectric tube actuator with hysteresis and creep
International Nuclear Information System (INIS)
Chung, S H; Fung, Eric H K
2010-01-01
Piezoelectric tube actuators are commonly used for nanopositioning in atomic force microscopes (AFMs). However, piezoelectric tube actuators exhibit hysteresis and creep which significantly limit the accuracy of nanopositioning. A finite element model of a piezoelectric tube actuator with hysteresis and creep is important for control purposes, but so far one has not been developed. The purpose of this paper is to present a nonlinear finite element (FE) model with hysteresis and creep for design purposes. Prandtl–Ishlinskii (PI) hysteresis operators and creep operators are adopted into constitutive equations. The nonlinear FE model is formulated using energy approach and Hamilton's principle. The parameters of the PI hysteresis operators and the creep operators are identified by comparing the simulation results and experimental results of other researchers. The working operation of the piezoelectric tube actuator is simulated by the reduced order FE model, and the displacement error due to hysteresis, creep and coupling effect is investigated. An output feedback controller is implemented into the reduced order FE model to show that this model is controllable
The Nonlinear Field Space Theory
Energy Technology Data Exchange (ETDEWEB)
Mielczarek, Jakub, E-mail: jakub.mielczarek@uj.edu.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Trześniewski, Tomasz, E-mail: tbwbt@ift.uni.wroc.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Institute for Theoretical Physics, University of Wrocław, pl. Borna 9, 50-204 Wrocław (Poland)
2016-08-10
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
The Nonlinear Field Space Theory
International Nuclear Information System (INIS)
Mielczarek, Jakub; Trześniewski, Tomasz
2016-01-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
International Nuclear Information System (INIS)
Walter, H.; Mang, H.A.
1991-01-01
A procedure for combining nonlinear short-time behavior of concrete with nonlinear creep compliance functions is presented. It is an important ingredient of a computer code for nonlinear finite element (FE) analysis of prestressed concrete shells, considering creep, shrinkage and ageing of concrete, and relaxation of the prestressing steel. The program was developed at the Institute for Strength of Materials of Technical University of Vienna, Austria. The procedure has resulted from efforts to extend the range of application of a Finite Element program, abbreviated as FESIA, which originally was capable of modeling reinforeced concrete in the context of thin-shell analysis, using nonlinear constitutive relations for both, conrete and steel. The extension encompasses the time-dependent behavior of concrete: Creep, shrinkage and ageing. Creep is modeled with the help of creep compliance functions which may be nonlinear to conform with the short-time constitutive relations. Ageing causes an interdependence between long-time and short-time deformations. The paper contains a description of the physical background of the procedure and hints on the implementation of the algorithm. The focus is on general aspects. Details of the aforementioned computer program are considered only where this is inevitable. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Lissenden, Cliff [Pennsylvania State Univ., State College, PA (United States); Hassan, Tasnin [North Carolina State Univ., Raleigh, NC (United States); Rangari, Vijaya [Tuskegee Univ., Tuskegee, AL (United States)
2014-10-30
The research built upon a prior investigation to develop a unified constitutive model for design-by-analysis of the intermediate heat exchanger (IHX) for a very high temperature reactor (VHTR) design of next generation nuclear plants (NGNPs). Model development requires a set of failure data from complex mechanical experiments to characterize the material behavior. Therefore uniaxial and multiaxial creep-fatigue and creep-ratcheting tests were conducted on the nickel-base Alloy 617 at 850 and 950°C. The time dependence of material behavior, and the interaction of time dependent behavior (e.g., creep) with ratcheting, which is an increase in the cyclic mean strain under load-controlled cycling, are major concerns for NGNP design. This research project aimed at characterizing the microstructure evolution mechanisms activated in Alloy 617 by mechanical loading and dwell times at elevated temperature. The acoustic harmonic generation method was researched for microstructural characterization. It is a nonlinear acoustics method with excellent potential for nondestructive evaluation, and even online continuous monitoring once high temperature sensors become available. It is unique because it has the ability to quantitatively characterize microstructural features well before macroscale defects (e.g., cracks) form. The nonlinear acoustics beta parameter was shown to correlate with microstructural evolution using a systematic approach to handle the complexity of multiaxial creep-fatigue and creep-ratcheting deformation. Mechanical testing was conducted to provide a full spectrum of data for: thermal aging, tensile creep, uniaxial fatigue, uniaxial creep-fatigue, uniaxial creep-ratcheting, multiaxial creep-fatigue, and multiaxial creep-ratcheting. Transmission Electron Microscopy (TEM), Scanning Electron Microscopy (SEM), and Optical Microscopy were conducted to correlate the beta parameter with individual microstructure mechanisms. We researched
International Nuclear Information System (INIS)
Lissenden, Cliff; Hassan, Tasnin; Rangari, Vijaya
2014-01-01
The research built upon a prior investigation to develop a unified constitutive model for design-@by-@analysis of the intermediate heat exchanger (IHX) for a very high temperature reactor (VHTR) design of next generation nuclear plants (NGNPs). Model development requires a set of failure data from complex mechanical experiments to characterize the material behavior. Therefore uniaxial and multiaxial creep-@fatigue and creep-@ratcheting tests were conducted on the nickel base Alloy 617 at 850 and 950°C. The time dependence of material behavior, and the interaction of time dependent behavior (e.g., creep) with ratcheting, which is an increase in the cyclic mean strain under load-@controlled cycling, are major concerns for NGNP design. This research project aimed at characterizing the microstructure evolution mechanisms activated in Alloy 617 by mechanical loading and dwell times at elevated temperature. The acoustic harmonic generation method was researched for microstructural characterization. It is a nonlinear acoustics method with excellent potential for nondestructive evaluation, and even online continuous monitoring once high temperature sensors become available. It is unique because it has the ability to quantitatively characterize microstructural features well before macroscale defects (e.g., cracks) form. The nonlinear acoustics beta parameter was shown to correlate with microstructural evolution using a systematic approach to handle the complexity of multiaxial creep-@fatigue and creep-@ratcheting deformation. Mechanical testing was conducted to provide a full spectrum of data for: thermal aging, tensile creep, uniaxial fatigue, uniaxial creep-@fatigue, uniaxial creep-ratcheting, multiaxial creep-fatigue, and multiaxial creep-@ratcheting. Transmission Electron Microscopy (TEM), Scanning Electron Microscopy (SEM), and Optical Microscopy were conducted to correlate the beta parameter with individual microstructure mechanisms. We researched application of the
Vortex creep and the internal temperature of neutron stars. I - General theory
Alpar, M. A.; Pines, D.; Anderson, P. W.; Shaham, J.
1984-01-01
The theory of a neutron star superfluid coupled to normal matter via thermal creep against pinning forces is developed in some detail. General equations of motion for a pinned rotating superfluid and their form for vortex creep are given. Steady state creep and the way in which the system approaches the steady state are discussed. The developed formalism is applied to the postglitch relaxation of a pulsar, and detailed models are developed which permit explicit calculation of the postglitch response. The energy dissipation associated with creep and glitches is considered.
A rationale for the observed non-linearity in pressure tube creep sag with time in service
International Nuclear Information System (INIS)
Sedran, P.J.
2013-01-01
In 2012, a paper was presented at the CNS SGC Conference which included an explanation for measured non-linear trends in Pressure Tube (PT) creep sag. The section of the 2012 paper covering this topic was revised and is presented as the main subject of this paper. The practical applications for the prediction of long-term Fuel Channel (FC) creep sag include the analysis of Calandria Tube - Liquid Injection Nozzle (CT-LIN) contact, and fuel passage and PT replacement assessments. The current practice for predicting FC creep sag in life cycle management applications is to use a linear model for creep sag versus time in service. However, PT sag measurements from the Point Lepreau Generating Station (PLGS) and Gentilly-2 (G-2) have displayed a non-linear trend with a creep sag rate that is decreasing with time in service. As an example, for PT F06 in PLGS, a 60% reduction in the nominal creep sag rate was observed for measurements taken 18 years apart. Subsequently, it was found that a 56% reduction in the creep sag rate for F06 over 18 years could be attributed to a fundamental geometric property of the PT creep sag profile. In addition, a further 1.6% decrease in the creep sag rate of the CT over the same period could be attributed to bending stress reductions due to the deformation of the CT. The resultant reduction in the PT creep sag rate for F06 was predicted to be 57.6%, closely matching the observed PT creep sag rate reduction of 60%. Therefore, this paper provides a rationale to explain the observed non-linear trends in PT creep sag, the use of which could benefit stations engaging in asset management as a means of FC life extension. This paper presents a summary of the worked performed to correlate the observed reductions in PT creep sag rate to the geometrical properties of the PT creep sag profile and the predicted bending stress reductions in the CT. (author)
Theory of void swelling, irradiation creep and growth
International Nuclear Information System (INIS)
Wood, M.H.; Bullough, R.; Hayns, M.R.
Recent progress in our understanding of the fundamental mechanisms involved in swelling, creep and growth of materials subjected to irradiation is reviewed. The topics discussed are: the sink types and their strengths in the lossy continuum; swelling and void distribution analysis, including recent work on void nucleation; and, irradiation creep and growth of zirconium and zircaloy are taken as an example
Kim, Gun; Loreto, Giovanni; Kim, Jin-Yeon; Kurtis, Kimberly E; Wall, James J; Jacobs, Laurence J
2018-08-01
This research conducts in situ nonlinear ultrasonic (NLU) measurements for real time monitoring of load-induced damage in concrete. For the in situ measurements on a cylindrical specimen under sustained load, a previously developed second harmonic generation (SHG) technique with non-contact detection is adapted to a cylindrical specimen geometry. This new setup is validated by demonstrating that the measured nonlinear Rayleigh wave signals are equivalent to those in a flat half space, and thus the acoustic nonlinearity parameter, β can be defined and interpreted in the same way. Both the acoustic nonlinearity parameter and strain are measured to quantitatively assess the early-age damage in a set of concrete specimens subjected to either 25 days of creep, or 11 cycles of cyclic loading at room temperature. The experimental results show that the acoustic nonlinearity parameter is sensitive to early-stage microcrack formation under both loading conditions - the measured β can be directly linked to the accumulated microscale damage. This paper demonstrates the potential of NLU for the in situ monitoring of mechanical load-induced microscale damage in concrete components. Copyright © 2018 Elsevier B.V. All rights reserved.
Spectral theory and nonlinear functional analysis
Lopez-Gomez, Julian
2001-01-01
This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems.The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.
A Geometrically—Nonlinear Plate Theory 12
Institute of Scientific and Technical Information of China (English)
AlbertC.J.LUO
1999-01-01
An approximate plate theory developed in this paper is based on an assumed displacement field,the strains described by a Taylor series in the normal distance from the middle surface,the exact strains of the middle surface and the equations of equilibrium governing the exact configuration of the deformed middle surface,In this theory the exact geometry of the deformed middle surface is used to derive the strains and equilibrium of the plate.Application of this theory does not depend on the constitutive law.THis theory can reduce to some existing nonlinear theories through imposition of constraints.
Nonlinear Lorentz-invariant theory of gravitation
International Nuclear Information System (INIS)
Petry, W.
1976-01-01
A nonlinear Lorentz-invariant theory of gravitation and a Lorentz-invariant Hamiltonian for a particle with spin in the gravitational field are developed. The equations of motions are studied. The theory is applied to the three well known tests of General Relativity. In the special case of the red shift of spectral lines and of the deflection of light, the theory gives the same results as the General Theory of Relativity, whereas in the case of the perihelion of the Mercury, the theory gives 40,3'', in good agreement with experimental results of Dicke. (author)
Nonlinearity and disorder: Theory and applications
DEFF Research Database (Denmark)
Bang, Ole; Sørensen, Mads Peter
Proceedings of the NATO Advanced Research Workshop (ARW) entitled Nonlinearity and Disorder: Theory and Applications, held in Tashkent, Uzbekistan, October 2-6, 2001. Phenomena of coherent structures in nonlinear systems and disorder are considered opposite in nature. For example one of the most...... of the photorefractive solitons. Another very fast growing area induced by the technological development is statistical phenomena in nonlinear pulse propagation in optical fibers. Intrinsic randomness of existing optical communication systems has an important impact on the performance of planned soliton communication...
Directory of Open Access Journals (Sweden)
D. K-S. Bataev
2015-01-01
Full Text Available Experimental data on the effect of the age of autoclaved aerated concrete with and without carbonation factor to change its physical and mechanical characteristics, as well as by the amount of creep deformation and degree of reversibility. It was found that the solution of applied problems creep theory for structures of autoclaved aerated concrete, in accordance with their carbonation from the effects of atmospheric carbon dioxide, it is necessary to use the theory of elastic-creeping body on the basis of function creep measures in the form proposed by prof. S.V. Alexandrovsky.
Theory and design of nonlinear metamaterials
Rose, Alec Daniel
If electronics are ever to be completely replaced by optics, a significant possibility in the wake of the fiber revolution, it is likely that nonlinear materials will play a central and enabling role. Indeed, nonlinear optics is the study of the mechanisms through which light can change the nature and properties of matter and, as a corollary, how one beam or color of light can manipulate another or even itself within such a material. However, of the many barriers preventing such a lofty goal, the narrow and limited range of properties supported by nonlinear materials, and natural materials in general, stands at the forefront. Many industries have turned instead to artificial and composite materials, with homogenizable metamaterials representing a recent extension of such composites into the electromagnetic domain. In particular, the inclusion of nonlinear elements has caused metamaterials research to spill over into the field of nonlinear optics. Through careful design of their constituent elements, nonlinear metamaterials are capable of supporting an unprecedented range of interactions, promising nonlinear devices of novel design and scale. In this context, I cast the basic properties of nonlinear metamaterials in the conventional formalism of nonlinear optics. Using alternately transfer matrices and coupled mode theory, I develop two complementary methods for characterizing and designing metamaterials with arbitrary nonlinear properties. Subsequently, I apply these methods in numerical studies of several canonical metamaterials, demonstrating enhanced electric and magnetic nonlinearities, as well as predicting the existence of nonlinear magnetoelectric and off-diagonal nonlinear tensors. I then introduce simultaneous design of the linear and nonlinear properties in the context of phase matching, outlining five different metamaterial phase matching methods, with special emphasis on the phase matching of counter propagating waves in mirrorless parametric amplifiers
Nonlinear theory of electroelastic and magnetoelastic interactions
Dorfmann, Luis
2014-01-01
This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.
International Nuclear Information System (INIS)
Mansur, L.K.; Yoo, M.H.
1979-01-01
The theory of void swelling and irradiation creep is now fairly comprehensive. A unifying concept on which most of this understanding rests is that of the rate theory point defect concentrations. Several basic aspects of this unifying conept are reviewed. These relate to local fluctuations in point defect concentrations produced by cascades, the effects of thermal and radiation-produced divacancies, and the effects of point defect trapping
A nonlinear theory of generalized functions
1990-01-01
This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applicati...
Quantitative theory of driven nonlinear brain dynamics.
Roberts, J A; Robinson, P A
2012-09-01
Strong periodic stimuli such as bright flashing lights evoke nonlinear responses in the brain and interact nonlinearly with ongoing cortical activity, but the underlying mechanisms for these phenomena are poorly understood at present. The dominant features of these experimentally observed dynamics are reproduced by the dynamics of a quantitative neural field model subject to periodic drive. Model power spectra over a range of drive frequencies show agreement with multiple features of experimental measurements, exhibiting nonlinear effects including entrainment over a range of frequencies around the natural alpha frequency f(α), subharmonic entrainment near 2f(α), and harmonic generation. Further analysis of the driven dynamics as a function of the drive parameters reveals rich nonlinear dynamics that is predicted to be observable in future experiments at high drive amplitude, including period doubling, bistable phase-locking, hysteresis, wave mixing, and chaos indicated by positive Lyapunov exponents. Moreover, photosensitive seizures are predicted for physiologically realistic model parameters yielding bistability between healthy and seizure dynamics. These results demonstrate the applicability of neural field models to the new regime of periodically driven nonlinear dynamics, enabling interpretation of experimental data in terms of specific generating mechanisms and providing new tests of the theory. Copyright © 2012 Elsevier Inc. All rights reserved.
Nonlinear system theory: another look at dependence.
Wu, Wei Biao
2005-10-04
Based on the nonlinear system theory, we introduce previously undescribed dependence measures for stationary causal processes. Our physical and predictive dependence measures quantify the degree of dependence of outputs on inputs in physical systems. The proposed dependence measures provide a natural framework for a limit theory for stationary processes. In particular, under conditions with quite simple forms, we present limit theorems for partial sums, empirical processes, and kernel density estimates. The conditions are mild and easily verifiable because they are directly related to the data-generating mechanisms.
le Graverend, J.-B.
2018-05-01
A lattice-misfit-dependent damage density function is developed to predict the non-linear accumulation of damage when a thermal jump from 1050 °C to 1200 °C is introduced somewhere in the creep life. Furthermore, a phenomenological model aimed at describing the evolution of the constrained lattice misfit during monotonous creep load is also formulated. The response of the lattice-misfit-dependent plasticity-coupled damage model is compared with the experimental results obtained at 140 and 160 MPa on the first generation Ni-based single crystal superalloy MC2. The comparison reveals that the damage model is well suited at 160 MPa and less at 140 MPa because the transfer of stress to the γ' phase occurs for stresses above 150 MPa which leads to larger variations and, therefore, larger effects of the constrained lattice misfit on the lifetime during thermo-mechanical loading.
Topics in nonlinear wave theory with applications
International Nuclear Information System (INIS)
Tracy, E.R.
1984-01-01
Selected topics in nonlinear wave theory are discussed, and applications to the study of modulational instabilities are presented. A historical survey is given of topics relating to solitons and modulational problems. A method is then presented for generating exact periodic and quasi-periodic solutions to several nonlinear wave equations, which have important physical applications. The method is then specialized for the purposes of studying the modulational instability of a plane wave solution of the nonlinear Schroedinger equation, an equation with general applicability in one-dimensional modulational problems. Some numerical results obtained in conjunction with the analytic study are presented. The analytic approach explains the recurrence phenomena seen in the numerical studies, and the numerical work of other authors. The method of solution (related to the inverse scattering method) is then analyzed within the context of Hamiltonian dynamics where it is shown that the method can be viewed as simply a pair of canonical transformations. The Abel Transformation, which appears here and in the work of other authors, is shown to be a special form of Liouville's transformation to action-angle variables. The construction of closed form solutions of these nonlinear wave equations, via the solution of Jacobi's inversion problem, is surveyed briefly
Nonlinear gravitons and curved twistor theory
International Nuclear Information System (INIS)
Penrose, R.
1976-01-01
A new approach to the quantization of general relativity is suggested in which a state consisting of just one graviton can be described, but in a way which involves both the curvature and nonlinearities of Einstein's theory. It is felt that this approach can be justified solely on its own merits but it also receives striking encouragement from another direction: a surprising mathematical result enables one to construct the general such nonlinear gravitation state from a curved twistor space, the construction being given in terms of one arbitrary holomorphic function of three complex variables. In this way, the approach fits naturally into the general twistor program for the description of quantized fields. (U.K.)
Nonlinear analysis approximation theory, optimization and applications
2014-01-01
Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.
International Nuclear Information System (INIS)
Paglietti, A.
1978-01-01
This paper is concerned with the thermodynamical theory of materials with fading memory exhibiting the creep and relaxation properties. It is shown that, once the current thermodynamical approach is followed, the second principle of thermodynamics implies for these materials further restrictions on the free-energy functional in addition to the well-known ones deduced in the general theory of materials with fading memory. The possibility of an experimental check of the current approach and the possibility of an alternative and more general approach are briefly discussed. (author)
Alternative theories of the non-linear negative mass instability
International Nuclear Information System (INIS)
Channell, P.J.
1974-01-01
A theory non-linear negative mass instability is extended to include resistance. The basic assumption is explained physically and an alternative theory is offered. The two theories are compared computationally. 7 refs., 8 figs
Czech Academy of Sciences Publication Activity Database
Dorigato, A.; Pegoretti, A.; Kolařík, Jan
2010-01-01
Roč. 31, č. 11 (2010), s. 1947-1955 ISSN 0272-8397 R&D Projects: GA ČR GA106/09/1348 Institutional research plan: CEZ:AV0Z40500505 Keywords : heterogeneous polymer blends * free-volume theory * copolymer blends Subject RIV: JI - Composite Materials Impact factor: 0.998, year: 2010
Nonlinear closed-loop control theory
International Nuclear Information System (INIS)
Perez, R.B.; Otaduy, P.J.; Abdalla, M.
1992-01-01
Traditionally, the control of nuclear power plants has been implemented by the use of proportional-integral (PI) control systems. PI controllers are both simple and, within their calibration range, highly reliable. However, PIs provide little performance information that could be used to diagnose out-of-range events or the nature of unanticipated transients that may occur in the plant. To go beyond the PI controller, the new control algorithms must deal with the physical system nonlinearities and with the reality of uncertain dynamics terms in its mathematical model. The tool to develop a new kind of control algorithm is provided by Optimal Control Theory. In this theory, a norm is minimized which incorporates the constraint that the model equations should be satisfied at all times by means of the Lagrange multipliers. Optimal control algorithms consist of two sets of coupled equations: (1) the model equations, integrated forward in time; and (2) the equations for the Lagrange multipliers (adjoints), integrated backwards in time. There are two challenges: dealing with large sets of coupled nonlinear equations and with a two-point boundary value problem that must be solved iteratively. In this paper, the rigorous conversion of the two-point boundary value problem into an initial value problem is presented. In addition, the incorporation into the control algorithm of ''real world'' constraints such as sensors and actuators, dynamic response functions and time lags introduced by the digitalization of analog signals is presented. (Author)
Gurbatov, S N; Saichev, A I
2012-01-01
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...
Creep collapse of TAPS fuel cladding
International Nuclear Information System (INIS)
Chaudhry, S.M.; Anand, A.K.
1975-01-01
Densification of UO 2 can cause axial gaps between fuel pelets and cladding in unsupported (internally) at these regions. An analysis is carried out regarding the possibility of creep collapse in these regions. The analysis is based on Timoshenko's theory of collapse. At various times during the residence of fuel in reactor following parameters are calculated : (1) inelastic collapse of perfectly circular tubes (2) plastic instability in oval tubes (3) effect of creep on ovality. Creep is considered to be a non-linear combination of the following : (a) thermal creep (b) intresenic creep (c) stress aided radiation enhanced (d) stress free growth (4) Critical pressure ratio. The results obtained are compared with G.E. predictions. The results do not predict collapse of TAPS fuel cladding for five year residence time. (author)
Spectral theory and nonlinear analysis with applications to spatial ecology
Cano-Casanova, S; Mora-Corral , C
2005-01-01
This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology. The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis - from the most abstract developments up to the most concrete applications to population dynamics and socio-biology - in an effort to fill the existing gaps between these fields.
Rigorous theory of molecular orientational nonlinear optics
International Nuclear Information System (INIS)
Kwak, Chong Hoon; Kim, Gun Yeup
2015-01-01
Classical statistical mechanics of the molecular optics theory proposed by Buckingham [A. D. Buckingham and J. A. Pople, Proc. Phys. Soc. A 68, 905 (1955)] has been extended to describe the field induced molecular orientational polarization effects on nonlinear optics. In this paper, we present the generalized molecular orientational nonlinear optical processes (MONLO) through the calculation of the classical orientational averaging using the Boltzmann type time-averaged orientational interaction energy in the randomly oriented molecular system under the influence of applied electric fields. The focal points of the calculation are (1) the derivation of rigorous tensorial components of the effective molecular hyperpolarizabilities, (2) the molecular orientational polarizations and the electronic polarizations including the well-known third-order dc polarization, dc electric field induced Kerr effect (dc Kerr effect), optical Kerr effect (OKE), dc electric field induced second harmonic generation (EFISH), degenerate four wave mixing (DFWM) and third harmonic generation (THG). We also present some of the new predictive MONLO processes. For second-order MONLO, second-order optical rectification (SOR), Pockels effect and difference frequency generation (DFG) are described in terms of the anisotropic coefficients of first hyperpolarizability. And, for third-order MONLO, third-order optical rectification (TOR), dc electric field induced difference frequency generation (EFIDFG) and pump-probe transmission are presented
Geometric Theory of Reduction of Nonlinear Control Systems
Elkin, V. I.
2018-02-01
The foundations of a differential geometric theory of nonlinear control systems are described on the basis of categorical concepts (isomorphism, factorization, restrictions) by analogy with classical mathematical theories (of linear spaces, groups, etc.).
Lectures in nonlinear mechanics and chaos theory
Stetz, Albert W
2016-01-01
This elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincaré in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing...
Perturbation Theory for Open Two-Level Nonlinear Quantum Systems
International Nuclear Information System (INIS)
Zhang Zhijie; Jiang Dongguang; Wang Wei
2011-01-01
Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r = C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results. (general)
Nonlinear structural mechanics theory, dynamical phenomena and modeling
Lacarbonara, Walter
2013-01-01
Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...
Nonlinear solar cycle forecasting: theory and perspectives
Baranovski, A. L.; Clette, F.; Nollau, V.
2008-02-01
In this paper we develop a modern approach to solar cycle forecasting, based on the mathematical theory of nonlinear dynamics. We start from the design of a static curve fitting model for the experimental yearly sunspot number series, over a time scale of 306 years, starting from year 1700 and we establish a least-squares optimal pulse shape of a solar cycle. The cycle-to-cycle evolution of the parameters of the cycle shape displays different patterns, such as a Gleissberg cycle and a strong anomaly in the cycle evolution during the Dalton minimum. In a second step, we extract a chaotic mapping for the successive values of one of the key model parameters - the rate of the exponential growth-decrease of the solar activity during the n-th cycle. We examine piece-wise linear techniques for the approximation of the derived mapping and we provide its probabilistic analysis: calculation of the invariant distribution and autocorrelation function. We find analytical relationships for the sunspot maxima and minima, as well as their occurrence times, as functions of chaotic values of the above parameter. Based on a Lyapunov spectrum analysis of the embedded mapping, we finally establish a horizon of predictability for the method, which allows us to give the most probable forecasting of the upcoming solar cycle 24, with an expected peak height of 93±21 occurring in 2011/2012.
Nonlinear solar cycle forecasting: theory and perspectives
Directory of Open Access Journals (Sweden)
A. L. Baranovski
2008-02-01
Full Text Available In this paper we develop a modern approach to solar cycle forecasting, based on the mathematical theory of nonlinear dynamics. We start from the design of a static curve fitting model for the experimental yearly sunspot number series, over a time scale of 306 years, starting from year 1700 and we establish a least-squares optimal pulse shape of a solar cycle. The cycle-to-cycle evolution of the parameters of the cycle shape displays different patterns, such as a Gleissberg cycle and a strong anomaly in the cycle evolution during the Dalton minimum. In a second step, we extract a chaotic mapping for the successive values of one of the key model parameters – the rate of the exponential growth-decrease of the solar activity during the n-th cycle. We examine piece-wise linear techniques for the approximation of the derived mapping and we provide its probabilistic analysis: calculation of the invariant distribution and autocorrelation function. We find analytical relationships for the sunspot maxima and minima, as well as their occurrence times, as functions of chaotic values of the above parameter. Based on a Lyapunov spectrum analysis of the embedded mapping, we finally establish a horizon of predictability for the method, which allows us to give the most probable forecasting of the upcoming solar cycle 24, with an expected peak height of 93±21 occurring in 2011/2012.
Charges in nonlinear higher-spin theory
Energy Technology Data Exchange (ETDEWEB)
Didenko, V.E. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation); Misuna, N.G. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation); Moscow Institute of Physics and Technology,Institutsky lane 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Vasiliev, M.A. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation)
2017-03-30
Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS{sub 4} Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.
Charges in nonlinear higher-spin theory
International Nuclear Information System (INIS)
Didenko, V.E.; Misuna, N.G.; Vasiliev, M.A.
2017-01-01
Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS 4 Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.
The constructive approach to nonlinear quantum field theory
International Nuclear Information System (INIS)
Segal, I.
1976-01-01
The general situation in nonlinear quantum field theory is outlined. The author discusses a reversion to the canonical quantization formalism and develops it to the maximal level attainable on the basis of advances in the past decade in nonlinear scattering and functional integration. (B.R.H.)
Nonlinear theory of the free-electron laser
International Nuclear Information System (INIS)
Chian, A.C.-L.; Padua Brito Serbeto, A. de.
1984-01-01
A theory of Raman free-electron laser using a circularly polarized electromagnetic pump is investigated. Coupled wave equations that describe both linear and nonlinear evolution of stimulated Raman scattering are derived. The dispersion relation and the growth rate for the parametric instability are obtained. Nonlinear processes that may lead to saturation of the free-electron laser are discussed. (Author) [pt
An introduction to nonlinear analysis and fixed point theory
Pathak, Hemant Kumar
2018-01-01
This book systematically introduces the theory of nonlinear analysis, providing an overview of topics such as geometry of Banach spaces, differential calculus in Banach spaces, monotone operators, and fixed point theorems. It also discusses degree theory, nonlinear matrix equations, control theory, differential and integral equations, and inclusions. The book presents surjectivity theorems, variational inequalities, stochastic game theory and mathematical biology, along with a large number of applications of these theories in various other disciplines. Nonlinear analysis is characterised by its applications in numerous interdisciplinary fields, ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to stochastic game theory. Organised into ten chapters, the book shows the elegance of the subject and its deep-rooted concepts and techniques, which provide the tools for developing more realistic and accurate models for ...
Theory of weakly nonlinear self-sustained detonations
Faria, Luiz; Kasimov, Aslan R.; Rosales, Rodolfo R.
2015-01-01
We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced
Nonlinear model predictive control theory and algorithms
Grüne, Lars
2017-01-01
This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...
Metallurgical principles of creep processes
International Nuclear Information System (INIS)
Bolton, C.J.
1977-12-01
A brief review is presented of current theories of a number of the physical processes which can be involved in deformation and fracture under creep conditions. The processes considered are power law creep, diffusion creep, grain boundary sliding, cavitation and other modes of failure, and creep crack growth. The note concludes with some suggestions for future work. (author)
On nonequilibrium many-body systems III: nonlinear transport theory
International Nuclear Information System (INIS)
Luzzi, R.; Vasconcellos, A.R.; Algarte, A.C.S.
1986-01-01
A nonlinear transport theory for many-body systems arbitrarily away from equilibrium, based on the nonequilibrium statistical operator (NSO) method, is presented. Nonlinear transport equations for a basis set of dynamical quantities are derived using two equivalent treatments that may be considered far reaching generalizations of the Hilbert-Chapman-Enskog method and Mori's generalized Langevin equations method. The first case is considered in some detail and the general characteristics of the theory are discussed. (Author) [pt
Nonlinear PI control of chaotic systems using singular perturbation theory
International Nuclear Information System (INIS)
Wang Jiang; Wang Jing; Li Huiyan
2005-01-01
In this paper, we develop the nonlinear PI controllers for a class of chaotic systems based on singular perturbation theory. The original system is decomposed into two reduced order systems, to which the nonlinear uncertain terms belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and combined to construct the composite controller for the full order system. The effectiveness and feasibility of the proposed control scheme is demonstrated through numerical simulations on the chaotic Chua's circuit
A SIPA-based theory of irradiation creep in the low swelling rate regime
International Nuclear Information System (INIS)
Garner, F.A.; Woo, C.H.
1991-11-01
A model is presented which describes the major facets of the relationships between irradiation creep, void swelling and applied stress. The increasing degree of anisotropy in distribution of dislocation Burger's vectors with stress level plays a major role in this model. Although bcc metals are known to creep and swell at lower rates than fcc metals, it is predicted that the creep-swelling coupling coefficient is actually larger
Nonlinear transport theory in the metal with tunnel barrier
Zubov, E. E.
2018-02-01
Within the framework of the scattering matrix formalism, the nonlinear Kubo theory for electron transport in the metal with a tunnel barrier has been considered. A general expression for the mean electrical current was obtained. It significantly simplifies the calculation of nonlinear contributions to the conductivity of various hybrid structures. In the model of the tunnel Hamiltonian, all linear and nonlinear contributions to a mean electrical current are evaluated. The linear approximation agrees with results of other theories. For effective barrier transmission ?, the ballistic transport is realised with a value of the Landauer conductivity equal to ?.
Energy flow theory of nonlinear dynamical systems with applications
Xing, Jing Tang
2015-01-01
This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...
Mathematical Systems Theory : from Behaviors to Nonlinear Control
Julius, A; Pasumarthy, Ramkrishna; Rapisarda, Paolo; Scherpen, Jacquelien
2015-01-01
This treatment of modern topics related to mathematical systems theory forms the proceedings of a workshop, Mathematical Systems Theory: From Behaviors to Nonlinear Control, held at the University of Groningen in July 2015. The workshop celebrated the work of Professors Arjan van der Schaft and Harry Trentelman, honouring their 60th Birthdays. The first volume of this two-volume work covers a variety of topics related to nonlinear and hybrid control systems. After giving a detailed account of the state of the art in the related topic, each chapter presents new results and discusses new directions. As such, this volume provides a broad picture of the theory of nonlinear and hybrid control systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participants’ ideas on exciting new approaches to control and system theory and their predictions of future directions for the subject that were discussed at the worksho...
Directory of Open Access Journals (Sweden)
Andrew V. Khokhlov
2017-04-01
Full Text Available The nonlinear Maxwell-type constitutive relation with two arbitrary material functions for viscoelastoplastic multi-modulus materials is studied analytically in uniaxial isothermic case to reveal the model abilities and applicability scope and to develop techniques of its identification, tuning and fitting. The constitutive equation is aimed at adequate modeling of the rheological phenomena set which is typical for reonomic materials exhibiting non-linear hereditary properties, strong strain rate sensitivity, secondary creep, yielding at constant stress, tension compression asymmetry and such temperature effects as increase of material compliance, strain rate sensitivity and rates of dissipation, relaxation, creep and plastic strain accumulation with temperature growth. The model is applicable for simulation of mechanical behaviour of various polymers, their solutions and melts, solid propellants, sand-asphalt concretes, composite materials, titanium and aluminum alloys, ceramics at high temperature and so on. To describe the influence of temperature on material mechanical behavior (under isothermic conditions, two scalar material parameters of the model (viscosity coefficient and “modulus of elasticity” are considered as a functions of temperature level. The general restrictions on their properties which are necessary and sufficient for adequate qualitative description of the basic thermomechanical phenomena related to typical temperature influence on creep and relaxation curves, creep recovery curves, creep curves under step-wise loading and quasi-static stress-strain curves of viscoelastoplastic materials are obtained. The restrictions are derived using systematic analytical study of general qualitative features of the theoretic creep and relaxation curves, creep curves under step-wise loading, long-term strength curves and stress-strain curves at constant strain or stress rates generated by the constitutive equation (under minimal
Overview of nonlinear theory of kinetically driven instabilities
International Nuclear Information System (INIS)
Berk, H.L.; Breizman, B.N.
1998-09-01
An overview is presented of the theory for the nonlinear behavior of instabilities driven by the resonant wave particle interaction. The approach should be applicable to a wide variety of kinetic systems in magnetic fusion devices and accelerators. Here the authors emphasize application to Alfven were driven instability, and the principles of the theory are used to interpret experimental data
Rusinko, Andrew; Varga, Peter
2018-04-01
The paper deals with modelling of the plastic and creep deformation of metals coupled with current. The passage of DC manifests itself in the increase in creep deformation and leads to primary creep time shortening. With plastic deformation, a short electric impulse results in the step-wise decrease of stress (stress-drop) on the stress-strain diagram. To catch these phenomena, we utilize the synthetic theory of recoverable deformation. The constitutive equation of this theory is supplemented by a term taking into account the intensity of DC. Further, we introduce DC intensity into the function governing transient creep. As a result, we predict the parameters of transient creep and calculate the stress-drop as a function of current intensity. The model results show good agreement with experimental data.
A Survey of Nonlinear Dynamics (Chaos Theory)
1991-04-01
example of an n = 1 Hamiltonian system does have separatrices. This is the 1D pendulum (Fig. 4.2): 9=p, p=-asin9;H(9,p) =p2 /2- acosO . (4-5) Phase space...method. There is no substitute for the actual labor of applying the nonlinear operator to a sum of normal modes, producing a general Galerkin vector
Nonlinear theory of localized standing waves
Denardo, Bruce; Larraza, Andrés; Putterman, Seth; Roberts, Paul
1992-01-01
An investigation of the nonlinear dispersive equations of continuum mechanics reveals localized standing-wave solutions that are domain walls between regions of different wave number. These states can appear even when the dispersion law is a single-valued function of the wave number. In addition, we calculate solutions for kinks in cutoff and noncutoff modes, as well as cutoff breather solitons. Division of Engineering and Geophysics of the Office of Basic Energy Science of U.S. DOE for su...
Nonlinear theory of collisionless trapped ion modes
International Nuclear Information System (INIS)
Hahm, T.S.; Tang, W.M.
1996-01-01
A simplified two field nonlinear model for collisionless trapped-ion-mode turbulence has been derived from nonlinear bounce-averaged drift kinetic equations. The renormalized thermal diffusivity obtained from this analysis exhibits a Bohm-like scaling. A new nonlinearity associated with the neoclassical polarization density is found to introduce an isotope-dependent modification to this Bohm-like diffusivity. The asymptotic balance between the equilibrium variation and the finite banana width induced reduction of the fluctuation potential leads to the result that the radial correlation length decreases with increasing plasma current. Other important conclusions from the present analysis include the predictions that (i) the relative density fluctuation level δn/n 0 is lower than the conventional mixing length estimate, Δr/L n (ii) the ion temperature fluctuation level δT i /T i significantly exceeds the density fluctuation level δn/n 0 ; and (iii) the parallel ion velocity fluctuation level δv iparallel /v Ti is expected to be negligible
An enstrophy-based linear and nonlinear receptivity theory
Sengupta, Aditi; Suman, V. K.; Sengupta, Tapan K.; Bhaumik, Swagata
2018-05-01
In the present research, a new theory of instability based on enstrophy is presented for incompressible flows. Explaining instability through enstrophy is counter-intuitive, as it has been usually associated with dissipation for the Navier-Stokes equation (NSE). This developed theory is valid for both linear and nonlinear stages of disturbance growth. A previously developed nonlinear theory of incompressible flow instability based on total mechanical energy described in the work of Sengupta et al. ["Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003)] is used to compare with the present enstrophy based theory. The developed equations for disturbance enstrophy and disturbance mechanical energy are derived from NSE without any simplifying assumptions, as compared to other classical linear/nonlinear theories. The theory is tested for bypass transition caused by free stream convecting vortex over a zero pressure gradient boundary layer. We explain the creation of smaller scales in the flow by a cascade of enstrophy, which creates rotationality, in general inhomogeneous flows. Linear and nonlinear versions of the theory help explain the vortex-induced instability problem under consideration.
An introduction to geometric theory of fully nonlinear parabolic equations
International Nuclear Information System (INIS)
Lunardi, A.
1991-01-01
We study a class of nonlinear evolution equations in general Banach space being an abstract version of fully nonlinear parabolic equations. In addition to results of existence, uniqueness and continuous dependence on the data, we give some qualitative results about stability of the stationary solutions, existence and stability of the periodic orbits. We apply such results to some parabolic problems arising from combustion theory. (author). 24 refs
Inverse operator theory method and its applications in nonlinear physics
International Nuclear Information System (INIS)
Fang Jinqing
1993-01-01
Inverse operator theory method, which has been developed by G. Adomian in recent years, and its applications in nonlinear physics are described systematically. The method can be an unified effective procedure for solution of nonlinear and/or stochastic continuous dynamical systems without usual restrictive assumption. It is realized by Mathematical Mechanization by us. It will have a profound on the modelling of problems of physics, mathematics, engineering, economics, biology, and so on. Some typical examples of the application are given and reviewed
Introduction to the theory of nonlinear optimization
Jahn, Johannes
2007-01-01
This book serves as an introductory text to optimization theory in normed spaces. The topics of this book are existence results, various differentiability notions together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a ba
International Nuclear Information System (INIS)
Skyrme, T.H.R.
1994-01-01
A unified field theory of mesons and their particle sources is proposed and considered in its classical aspects. The theory has static solutions of a singular nature, but finite energy, characterized by spin directions; the number of such entities is a rigorously conserved constant of motion; they interact with an external meson field through a derivative-type coupling with the spins, akin to the formalism of strong-coupling meson theory. There is a conserved current identifiable with isobaric spin, and another that may be related to hypercharge. The postulates include one constant of the dimensions of length, and another that is conjecture necessarily to have the value (h/2π)c, or perhaps 1/2(h/2π)c, in the quantized theory. (author). 5 refs
Quantization of a nonlinearly realized supersymmetric theory
International Nuclear Information System (INIS)
Shima, K.
1977-01-01
The two-dimensional version of the Volkov-Akulov Lagrangian, where the supersymmetry is realized nonlinearly by means of a single Majorana spinor psi (x), is quantized. The equal-time anticommutators for the field are not c numbers but are functions of the field itself. By explicit calculation we shall show that the supersymmetry charges of the model form the supersymmetry algebra (the graded Lie algebra); therefore the Hamiltonian of the system P 0 is written as a bilinear sum of products of supersymmetry charges. We shall also show that the supersymmetry charges exactly generate a constant translation of psi (x) in the spinor space
Linear and Nonlinear Theories of Cosmic Ray Transport
International Nuclear Information System (INIS)
Shalchi, A.
2005-01-01
The transport of charged cosmic rays in plasmawave turbulence is a modern and interesting field of research. We are mainly interested in spatial diffusion parallel and perpendicular to a large scale magnetic field. During the last decades quasilinear theory was the standard tool for the calculation of diffusion coefficients. Through comparison with numerical simulations we found several cases where quasilinear theory is invalid. On could define three major problems of transport theory. I will demonstrate that new nonlinear theories which were proposed recently can solve at least some to these problems
Theory for Nonlinear Spectroscopy of Vibrational Polaritons
Ribeiro, RF; Dunkelberger, AD; Xiang, B; Xiong, W; Simpkins, BS; Owrutsky, JC; Yuen-Zhou, J
2017-01-01
Molecular polaritons have gained considerable attention due to their potential to control nanoscale molecular processes by harnessing electromagnetic coherence. Although recent experiments with liquid-phase vibrational polaritons have shown great promise for exploiting these effects, significant challenges remain in interpreting their spectroscopic signatures. In this letter, we develop a quantum-mechanical theory of pump-probe spectroscopy for this class of polaritons based on the quantum La...
Nonlinear neoclassical theory for toroidal edge plasmas
International Nuclear Information System (INIS)
Fueloep, T.; Helander, P.
2001-01-01
Edge plasma processes play a critical role for the global confinement of the plasma. In the edge region, where impurity ions are abundant and the temperature and density gradients are large, the assumptions of the standard neoclassical theory break down. We have extended the theory of neoclassical transport in an impure plasma with arbitrary cross section and aspect ratio to allow for steeper pressure and temperature gradients than are usually considered in the conventional theory. The gradients are allowed to be so large that the friction force between the bulk ions and heavy impurities is comparable to the parallel impurity pressure gradient. In this case the impurity ions are found to undergo a spontaneous rearrangement on each flux surface. This reduces their parallel friction with the bulk ions and causes the neoclassical ion flux to become a non-monotonic function of the gradients for plasma parameters typical of the tokamak edge. Thus, the neoclassical confinement is improved in regions where the gradients are large, such as in the edge pedestal. The theoretical predictions are compared with experimental data from several tokamaks. (orig.)
Soliton excitations in a class of nonlinear field theory models
International Nuclear Information System (INIS)
Makhan'kov, V.G.; Fedyanin, V.K.
1985-01-01
Investigation results of nonlinear models of the field theory with a lagrangian are described. The theory includes models both with zero stable vacuum epsilon=1 and with condensate epsilon=-1 (of disturbed symmetry). Conditions of existence of particle-like solutions (PLS), stability of these solutions are investigated. Soliton dynamics is studied. PLS formfactors are calculated. Statistical mechanics of solitons is built and their dynamic structure factors are calculated
A new integrability theory for certain nonlinear physical problems
International Nuclear Information System (INIS)
Berger, M.S.
1993-01-01
A new mathematically sound integrability theory for certain nonlinear problems defined by ordinary or partial differential equations is defined. The new theory works in an arbitrary finite number of space dimensions. Moreover, if a system is integrable in the new sense described here, it has a remarkable stability property that distinguishes if from any previously known integrability ideas. The new theory proceeds by establishing a ''global normal form'' for the problem at hand. This normal form holds subject to canonical coordinate transformations, extending such classical ideas by using new nonlinear methods of infinite dimensional functional analysis. The global normal form in question is related to the mathematical theory of singularities of mappings of H. Whitney and R. Thom extended globally and form finite to infinite dimensions. Thus bifurcation phenomena are naturally included in the new integrability theory. Typical examples include the classically nonintegrable Riccati equation, certain non-Euclidean mean field theories, certain parabolic reaction diffusion equations and the hyperbolic nonlinear telegrapher's equation. (Author)
de Sitter limit of inflation and nonlinear perturbation theory
DEFF Research Database (Denmark)
R. Jarnhus, Philip; Sloth, Martin Snoager
2007-01-01
We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gaug...
Non-linear theory of elasticity
Lurie, AI
2012-01-01
This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.
Energy Technology Data Exchange (ETDEWEB)
Galindo-Nava, E.I., E-mail: eg375@cam.ac.uk; Rae, C.M.F.
2016-01-10
A new approach for modelling dislocation creep during primary and secondary creep in FCC metals is proposed. The Orowan equation and dislocation behaviour at the grain scale are revisited to include the effects of different microstructures such as the grain size and solute atoms. Dislocation activity is proposed to follow a jog-diffusion law. It is shown that the activation energy for cross-slip E{sub cs} controls dislocation mobility and the strain increments during secondary creep. This is confirmed by successfully comparing E{sub cs} with the experimentally determined activation energy during secondary creep in 5 FCC metals. It is shown that the inverse relationship between the grain size and dislocation creep is attributed to the higher number of strain increments at the grain level dominating their magnitude as the grain size decreases. An alternative approach describing solid solution strengthening effects in nickel alloys is presented, where the dislocation mobility is reduced by dislocation pinning around solute atoms. An analysis on the solid solution strengthening effects of typical elements employed in Ni-base superalloys is also discussed. The model results are validated against measurements of Cu, Ni, Ti and 4 Ni-base alloys for wide deformation conditions and different grain sizes.
Backward stochastic differential equations from linear to fully nonlinear theory
Zhang, Jianfeng
2017-01-01
This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.
Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.
Meair, Jonathan; Jacquod, Philippe
2013-02-27
We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance.
SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics
Energy Technology Data Exchange (ETDEWEB)
Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.
1998-09-01
This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.
Properties of some nonlinear Schroedinger equations motivated through information theory
International Nuclear Information System (INIS)
Yuan, Liew Ding; Parwani, Rajesh R
2009-01-01
We update our understanding of nonlinear Schroedinger equations motivated through information theory. In particular we show that a q-deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system, thus favouring the simplest q = 1 case. Furthermore the energy minimisation criterion is shown to be equivalent, at leading order, to an uncertainty maximisation argument. The special value η = 1/4 for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, η might be encoding relativistic effects.
Microprestress-Solidification Theory for Concrete Creep. I: Aging and Drying Effects
DEFF Research Database (Denmark)
Bazant, Z.P.; Hauggaard-Nielsen, Anders Boe; Baweja, S.
1997-01-01
microprestress carried by the bonds and bridges crossing the micropores (gel pores) in the hardened cement gel. The microprestress is generated by the disjoining pressure of the hindered adsorbed water in the micropores and by very large and highly localized volume changes caused by hydration or drying. The long......-term creep, deviatoric as well as volumetric, is assumed to originate from viscous shear slips between the opposite walls of the micropores in which the bonds or bridges that cross the micropores (and transmit the microprestress) break and reform. The long-term aging exhibited by the flow term in the creep...
Frehner, Marcel; Amschwand, Dominik; Gärtner-Roer, Isabelle
2016-04-01
Rockglaciers consist of unconsolidated rock fragments (silt/sand-rock boulders) with interstitial ice; hence their creep behavior (i.e., rheology) may deviate from the simple and well-known flow-laws for pure ice. Here we constrain the non-linear viscous flow law that governs rockglacier creep based on geomorphological observations. We use the Murtèl rockglacier (upper Engadin valley, SE Switzerland) as a case study, for which high-resolution digital elevation models (DEM), time-lapse borehole deformation data, and geophysical soundings exist that reveal the exterior and interior architecture and dynamics of the landform. Rockglaciers often feature a prominent furrow-and-ridge topography. For the Murtèl rockglacier, Frehner et al. (2015) reproduced the wavelength, amplitude, and distribution of the furrow-and-ridge morphology using a linear viscous (Newtonian) flow model. Arenson et al. (2002) presented borehole deformation data, which highlight the basal shear zone at about 30 m depth and a curved deformation profile above the shear zone. Similarly, the furrow-and-ridge morphology also exhibits a curved geometry in map view. Hence, the surface morphology and the borehole deformation data together describe a curved 3D geometry, which is close to, but not quite parabolic. We use a high-resolution DEM to quantify the curved geometry of the Murtèl furrow-and-ridge morphology. We then calculate theoretical 3D flow geometries using different non-linear viscous flow laws. By comparing them to the measured curved 3D geometry (i.e., both surface morphology and borehole deformation data), we can determine the most adequate flow-law that fits the natural data best. Linear viscous models result in perfectly parabolic flow geometries; non-linear creep leads to localized deformation at the sides and bottom of the rockglacier while the deformation in the interior and top are less intense. In other words, non-linear creep results in non-parabolic flow geometries. Both the
Effective-medium theory for nonlinear magneto-optics in magnetic granular alloys: cubic nonlinearity
International Nuclear Information System (INIS)
Granovsky, Alexander B.; Kuzmichov, Michail V.; Clerc, J.-P.; Inoue, Mitsuteru
2003-01-01
We propose a simple effective-medium approach for calculating the effective dielectric function of a magnetic metal-insulator granular alloy in which there is a weakly nonlinear relation between electric displacement D and electric field E for both constituent materials of the form D i =ε i (0) E i +χ i (3) |E i | 2 E i . We assume that linear ε i (0) and cubic nonlinear χ i (3) dielectric functions are diagonal and linear with magnetization non-diagonal components. For such metal-insulator composite magneto-optical effects depend on a light intensity and the effective cubic dielectric function χ eff (3) can be significantly greater (up to 10 3 times) than that for constituent materials. The calculation scheme is based on the Bergman and Stroud-Hui theory of nonlinear optical properties of granular matter. The giant cubic magneto-optical nonlinearity is found for composites with metallic volume fraction close to the percolation threshold and at a resonance of optical conductivity. It is shown that a composite may exhibit nonlinear magneto-optics even when both constituent materials have no cubic magneto-optical nonlinearity
Effective-medium theory for nonlinear magneto-optics in magnetic granular alloys: cubic nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Granovsky, Alexander B. E-mail: granov@magn.ru; Kuzmichov, Michail V.; Clerc, J.-P.; Inoue, Mitsuteru
2003-03-01
We propose a simple effective-medium approach for calculating the effective dielectric function of a magnetic metal-insulator granular alloy in which there is a weakly nonlinear relation between electric displacement D and electric field E for both constituent materials of the form D{sub i}={epsilon}{sub i}{sup (0)}E{sub i} +{chi}{sub i}{sup (3)}|E{sub i}|{sup 2}E{sub i}. We assume that linear {epsilon}{sub i}{sup (0)} and cubic nonlinear {chi}{sub i}{sup (3)} dielectric functions are diagonal and linear with magnetization non-diagonal components. For such metal-insulator composite magneto-optical effects depend on a light intensity and the effective cubic dielectric function {chi}{sub eff}{sup (3)} can be significantly greater (up to 10{sup 3} times) than that for constituent materials. The calculation scheme is based on the Bergman and Stroud-Hui theory of nonlinear optical properties of granular matter. The giant cubic magneto-optical nonlinearity is found for composites with metallic volume fraction close to the percolation threshold and at a resonance of optical conductivity. It is shown that a composite may exhibit nonlinear magneto-optics even when both constituent materials have no cubic magneto-optical nonlinearity.
Nonlinear turbulence theory and simulation of Buneman instability
International Nuclear Information System (INIS)
Yoon, P. H.; Umeda, T.
2010-01-01
In the present paper, the weak turbulence theory for reactive instabilities, formulated in a companion paper [P. H. Yoon, Phys. Plasmas 17, 112316 (2010)], is applied to the strong electron-ion two-stream (or Buneman) instability. The self-consistent theory involves quasilinear velocity space diffusion equation for the particles and nonlinear wave kinetic equation that includes quasilinear (or induced emission) term as well as nonlinear wave-particle interaction term (or a term that represents an induced scattering off ions). We have also performed one-dimensional electrostatic Vlasov simulation in order to benchmark the theoretical analysis. Under the assumption of self-similar drifting Gaussian distribution function for the electrons it is shown that the current reduction and the accompanying electron heating as well as electric field turbulence generation can be discussed in a self-consistent manner. Upon comparison with the Vlasov simulation result it is found that quasilinear wave kinetic equation alone is insufficient to account for the final saturation amplitude. Upon including the nonlinear scattering term in the wave kinetic equation, however, we find that a qualitative agreement with the simulation is recovered. From this, we conclude that the combined quasilinear particle diffusion plus induced emission and scattering (off ions) processes adequately account for the nonlinear development of the Buneman instability.
Information theory and stochastics for multiscale nonlinear systems
Majda, Andrew J; Grote, Marcus J
2005-01-01
This book introduces mathematicians to the fascinating emerging mathematical interplay between ideas from stochastics and information theory and important practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of com...
Composite Beam Theory with Material Nonlinearities and Progressive Damage
Jiang, Fang
Beam has historically found its broad applications. Nowadays, many engineering constructions still rely on this type of structure which could be made of anisotropic and heterogeneous materials. These applications motivate the development of beam theory in which the impact of material nonlinearities and damage on the global constitutive behavior has been a focus in recent years. Reliable predictions of these nonlinear beam responses depend on not only the quality of the material description but also a comprehensively generalized multiscale methodology which fills the theoretical gaps between the scales in an efficient yet high-fidelity manner. The conventional beam modeling methodologies which are built upon ad hoc assumptions are in lack of such reliability in need. Therefore, the focus of this dissertation is to create a reliable yet efficient method and the corresponding tool for composite beam modeling. A nonlinear beam theory is developed based on the Mechanics of Structure Genome (MSG) using the variational asymptotic method (VAM). The three-dimensional (3D) nonlinear continuum problem is rigorously reduced to a one-dimensional (1D) beam model and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities by exploiting the small geometric parameter which is an inherent geometric characteristic of the beam. The 2D nonlinear cross-sectional analysis utilizes the 3D material models to homogenize the beam cross-sectional constitutive responses considering the nonlinear elasticity and progressive damage. The results from such a homogenization are inputs as constitutive laws into the global nonlinear 1D beam analysis. The theoretical foundation is formulated without unnecessary kinematic assumptions. Curvilinear coordinates and vector calculus are utilized to build the 3D deformation gradient tensor, of which the components are formulated in terms of cross-sectional coordinates, generalized beam strains, unknown warping
A general sensitivity theory for simulations of nonlinear systems
International Nuclear Information System (INIS)
Kenton, M.A.
1981-01-01
A general sensitivity theory is developed for nonlinear lumped-parameter system simulations. The point-of-departure is general perturbation theory, which has long been used for linear systems in nuclear engineering and reactor physics. The theory allows the sensitivity of particular figures-of-merit of the system behavior to be calculated with respect to any parameter.An explicit procedure is derived for applying the theory to physical systems undergoing sudden events (e.g., reactor scrams, tank ruptures). A related problem, treating figures-of-merit defined as functions of extremal values of system variables occurring at sudden events, is handled by the same procedure. The general calculational scheme for applying the theory to numerical codes is discussed. It is shown that codes which use pre-packaged implicit integration subroutines can be augmented to include sensitivity theory: a companion set of subroutines to solve the sensitivity problem is listed. This combined system analysis code is applied to a simple model for loss of post-accident heat removal in a liquid metal-cooled fast breeder reactor. The uses of the theory for answering more general sensitivity questions are discussed. One application of the theory is to systematically determine whether specific physical processes in a model contribute significantly to the figures-of-merit. Another application of the theory is for selecting parameter values which enable a model to match experimentally observed behavior
The preparation problem in nonlinear extensions of quantum theory
Cavalcanti, Eric G.; Menicucci, Nicolas C.; Pienaar, Jacques L.
2012-01-01
Nonlinear modifications to the laws of quantum mechanics have been proposed as a possible way to consistently describe information processing in the presence of closed timelike curves. These have recently generated controversy due to possible exotic information-theoretic effects, including breaking quantum cryptography and radically speeding up both classical and quantum computers. The physical interpretation of such theories, however, is still unclear. We consider a large class of operationa...
Second quantization of classical nonlinear relativistic field theory. Pt. 2
International Nuclear Information System (INIS)
Balaban, T.
1976-01-01
The construction of a relativistic interacting local quantum field is given in two steps: first the classical nonlinear relativistic field theory is written down in terms of Poisson brackets, with initial conditions as canonical variables: next a representation of Poisson bracket Lie algebra by means of linear operators in the topological vector space is given and an explicit form of a local interacting relativistic quantum field PHI is obtained. (orig./BJ) [de
Two-dimensional nonlinear equations of supersymmetric gauge theories
International Nuclear Information System (INIS)
Savel'ev, M.V.
1985-01-01
Supersymmetric generalization of two-dimensional nonlinear dynamical equations of gauge theories is presented. The nontrivial dynamics of a physical system in the supersymmetry and supergravity theories for (2+2)-dimensions is described by the integrable embeddings of Vsub(2/2) superspace into the flat enveloping superspace Rsub(N/M), supplied with the structure of a Lie superalgebra. An equation is derived which describes a supersymmetric generalization of the two-dimensional Toda lattice. It contains both super-Liouville and Sinh-Gordon equations
Synthesis of robust nonlinear autopilots using differential game theory
Menon, P. K. A.
1991-01-01
A synthesis technique for handling unmodeled disturbances in nonlinear control law synthesis was advanced using differential game theory. Two types of modeling inaccuracies can be included in the formulation. The first is a bias-type error, while the second is the scale-factor-type error in the control variables. The disturbances were assumed to satisfy an integral inequality constraint. Additionally, it was assumed that they act in such a way as to maximize a quadratic performance index. Expressions for optimal control and worst-case disturbance were then obtained using optimal control theory.
Development of a nonlinear unsteady transonic flow theory
Stahara, S. S.; Spreiter, J. R.
1973-01-01
A nonlinear, unsteady, small-disturbance theory capable of predicting inviscid transonic flows about aerodynamic configurations undergoing both rigid body and elastic oscillations was developed. The theory is based on the concept of dividing the flow into steady and unsteady components and then solving, by method of local linearization, the coupled differential equation for unsteady surface pressure distribution. The equations, valid at all frequencies, were derived for two-dimensional flows, numerical results, were obtained for two classses of airfoils and two types of oscillatory motions.
Nonlinear dynamical systems for theory and research in ergonomics.
Guastello, Stephen J
2017-02-01
Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system. Practitioner Summary: Nonlinear dynamical systems theory reframes problems in ergonomics that involve complex systems as they change over time. The leading applications to date include psychophysics, control theory, cognitive workload and fatigue, biomechanics, occupational accidents, resilience of systems, team coordination and synchronisation of system components.
International Nuclear Information System (INIS)
Matsuda, Akihiro; Yabana, Shuichi
2000-01-01
In this report, to evaluate creep properties and effects of creep deformation on mechanical properties of thick rubber bearings for three-dimensional isolation system, we show results of compression creep test for rubber bearings of various rubber materials and shapes and development of numerical simulation method. Creep properties of thick rubber bearings were obtained from compression creep tests. The creep strain shows steady creep that have logarithmic relationships between strain and time and accelerated creep that have linear relationships. We make numerical model of a rubber material with nonlinear viscoelastic constitutional equations. Mechanical properties after creep loading test are simulated with enough accuracy. (author)
International Nuclear Information System (INIS)
Stone, C.M.; Nickell, R.E.
1977-01-01
Because of the characteristics of LMFBR primary piping components (thin-walled, low pressure, high temperature), the designer must guard against creep buckling as a potential failure mode for certain critical regions, such as elbows, where structural flexibility and inelastic response may combine to concentrate deformation and cause instability. The ASME Boiler and Pressure Vessel Code, through its elevated temperature Code Case 1592 (Section III, Division 1) provides design rules for Class 1 components aimed at preventing creep buckling during the design life. A similar set of rules is being developed for Class 2 and 3 components at this time. One of the original concepts behind the creep buckling rules was that the variability in creep properties (especially due to the effects of prior heat treatment), the uncertainty about initial imperfections, and the lack of confirmed accuracy of design analysis meant that conservatism would be difficult to assure. As a result, a factor of ten on service life was required (i.e. analysis must show that, under service conditions that extrapolate the life of the component by ten times, creep buckling does not occur). Two obvious problems with this approach are that: first, the creep behavior must also be extrapolated (since most creep experiments are terminated at a small fraction of the design life, extrapolation of creep data is already an issue, irrespective of the creep buckling question); second the nonlinear creep analysis, which is very nearly prohibitively expensive for design life histograms, becomes even more costly. Analytical results for an aluminum cylindrical shell subjected to axial loads at elevated temperatures are used to examine the supposed equivalence of two types of time-dependent buckling safety factors - a factor of ten on service life and a factor of 1.5 on loading
Irradiation creep models - an overview
International Nuclear Information System (INIS)
Matthews, J.R.; Finnis, M.W.
1988-01-01
The modelling of irradiation creep is now highly developed but many of the basic processes underlying the models are poorly understood. A brief introduction is given to the theory of cascade interactions, point defect clustering and dislocation climb. The range of simple irradiation creep models is reviewed including: preferred nucleation of interstitial loops; preferred absorption of point defects by dislocations favourably orientated to an applied stress; various climb-enhanced glide and recovery mechanisms, and creep driven by internal stresses produced by irradiation growth. A range of special topics is discussed including: cascade effects; creep transients; structural and induced anisotropy; and the effect of impurities. The interplay between swelling and growth with thermal and irradiation creep is emphasized. A discussion is given on how irradiation creep theory should best be developed to assist the interpretation of irradiation creep observations and the requirements of reactor designers. (orig.)
On the non-linear scale of cosmological perturbation theory
Blas, Diego; Konstandin, Thomas
2013-01-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Nonlinear responses of chiral fluids from kinetic theory
Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun
2018-01-01
The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.
On the non-linear scale of cosmological perturbation theory
International Nuclear Information System (INIS)
Blas, Diego; Garny, Mathias; Konstandin, Thomas
2013-04-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Theories of quantum dissipation and nonlinear coupling bath descriptors
Xu, Rui-Xue; Liu, Yang; Zhang, Hou-Dao; Yan, YiJing
2018-03-01
The quest of an exact and nonperturbative treatment of quantum dissipation in nonlinear coupling environments remains in general an intractable task. In this work, we address the key issues toward the solutions to the lowest nonlinear environment, a harmonic bath coupled both linearly and quadratically with an arbitrary system. To determine the bath coupling descriptors, we propose a physical mapping scheme, together with the prescription reference invariance requirement. We then adopt a recently developed dissipaton equation of motion theory [R. X. Xu et al., Chin. J. Chem. Phys. 30, 395 (2017)], with the underlying statistical quasi-particle ("dissipaton") algebra being extended to the quadratic bath coupling. We report the numerical results on a two-level system dynamics and absorption and emission line shapes.
Non-linear theory of elasticity and optimal design
Ratner, LW
2003-01-01
In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it
The creep bending of short radius pipe bends
International Nuclear Information System (INIS)
Spence, John
1975-01-01
In existing and proposed liquid metal fast breeder reactor design the pipework has considerable importance. Parts of the LMFBR include thin walled short radius bends which are expected to operate in the creep regime. In linear elasticity it is known that the assumption of long radius bends is not too severe as far as the flexibility characteristics are concerned although some modifications are necessary for accurate determination of the stresses. No data exists for nonlinear creep. Current work is aimed at elucidating the effect of the various assumptions common to linear elastic theory in so far as they affect the creep characteristics of bends on systems. Herein an energy based analysis using a simple n power constitutive law for stationary creep is employed to derive basic design data for flexibilities and stresses which will be necessary before complete systems can be assessed for creep. The analysis shows on comparison with the long radius work that the assumption of R>r is not much more restrictive in creep than for linear elasticity. Flexibilities for short radius bends appear to be well approximated by the long radius values. Thus the attractive reference stress information already derived may be used directly to find deformations without a complete knowledge of the constitutive relationship. However, stresses are somewhat different. Fortunately the maximum deviation occurs at relatively low levels of stress, the peak stresses being in fair agreement. When n=1 the present results reduce essentially to those obtained from existing linear elastic theory
Nonlinear electroelasticity: material properties, continuum theory and applications.
Dorfmann, Luis; Ogden, Ray W
2017-08-01
In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.
Nonlinear electroelasticity: material properties, continuum theory and applications
Dorfmann, Luis; Ogden, Ray W.
2017-08-01
In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.
Analytic theory of the nonlinear M = 1 tearing mode
International Nuclear Information System (INIS)
Hazeltine, R.D.; Meiss, J.D.; Morrison, P.J.
1985-09-01
Numerical studies show that the m = 1 tearing mode continues to grow exponentially well into the nonlinear regime, in contrast with the slow, ''Rutherford,'' growth of m > 1 modes. We present a single helicity calculation which generalizes that of Rutherford to the case when the constant-psi approximation is invalid. As in that theory, the parallel current becomes an approximate flux function when the island size, W, exceeds the linear tearing layer width. However for the m = 1 mode, W becomes proportional to deltaB, rather than (deltaB)/sup 1/2/ above this critical amplitude. This implies that the convective nonlinearity in Ohm's law, which couples the m = 0 component to the m = 1 component, dominates the resistive diffusion term. The balance between the inductive electric field and this convective nonlinearity results in exponential growth. Assuming the form of the perturbed fields to be like that of the linear mode, we find that the growth occurs at 71% of the linear rate
Nonlinear closure relations theory for transport processes in nonequilibrium systems
International Nuclear Information System (INIS)
Sonnino, Giorgio
2009-01-01
A decade ago, a macroscopic theory for closure relations has been proposed for systems out of Onsager's region. This theory is referred to as the thermodynamic field theory (TFT). The aim of this work was to determine the nonlinear flux-force relations that respect the thermodynamic theorems for systems far from equilibrium. We propose a formulation of the TFT where one of the basic restrictions, namely, the closed-form solution for the skew-symmetric piece of the transport coefficients, has been removed. In addition, the general covariance principle is replaced by the De Donder-Prigogine thermodynamic covariance principle (TCP). The introduction of TCP requires the application of an appropriate mathematical formalism, which is referred to as the entropy-covariant formalism. By geometrical arguments, we prove the validity of the Glansdorff-Prigogine universal criterion of evolution. A new set of closure equations determining the nonlinear corrections to the linear ('Onsager') transport coefficients is also derived. The geometry of the thermodynamic space is non-Riemannian. However, it tends to be Riemannian for high values of the entropy production. In this limit, we recover the transport equations found by the old theory. Applications of our approach to transport in magnetically confined plasmas, materials submitted to temperature, and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein. Transport processes in tokamak plasmas are of particular interest. In this case, even in the absence of turbulence, the state of the plasma remains close to (but, it is not in) a state of local equilibrium. This prevents the transport relations from being linear.
Nonlinear mean field theory for nuclear matter and surface properties
International Nuclear Information System (INIS)
Boguta, J.; Moszkowski, S.A.
1983-01-01
Nuclear matter properties are studied in a nonlinear relativistic mean field theory. We determine the parameters of the model from bulk properties of symmetric nuclear matter and a reasonable value of the effective mass. In this work, we stress the nonrelativistic limit of the theory which is essentially equivalent to a Skyrme hamiltonian, and we show that most of the results can be obtained, to a good approximation, analytically. The strength of the required parameters is determined from the binding energy and density of nuclear matter and the effective nucleon mass. For realistic values of the parameters, the nonrelativistic approximation turns out to be quite satisfactory. Using reasonable values of the parameters, we can account for other key properties of nuclei, such as the spin-orbit coupling, surface energy, and diffuseness of the nuclear surface. Also the energy dependence of the nucleon-nucleus optical model is accounted for reasonably well except near the Fermi surface. It is found, in agreement with empirical results, that the Landau parameter F 0 is quite small in normal nuclear matter. Both density dependence and momentum dependence of the NN interaction, but especially the former, are important for nuclear saturation. The required scalar and vector coupling constants agree fairly well with those obtained from analyses of NN scattering phase shifts with one-boson-exchange models. The mean field theory provides a semiquantitative justification for the weak Skyrme interaction in odd states. The strength of the required nonlinear term is roughly consistent with that derived using a new version of the chiral mean field theory in which the vector mass as well as the nucleon mass is generated by the sigma-field. (orig.)
A non-linear theory of strong interactions
International Nuclear Information System (INIS)
Skyrme, T.H.R.
1994-01-01
A non-linear theory of mesons, nucleons and hyperons is proposed. The three independent fields of the usual symmetrical pseudo-scalar pion field are replaced by the three directions of a four-component field vector of constant length, conceived in an Euclidean four-dimensional isotopic spin space. This length provides the universal scaling factor, all other constants being dimensionless; the mass of the meson field is generated by a φ 4 term; this destroys the continuous rotation group in the iso-space, leaving a 'cubic' symmetry group. Classification of states by this group introduces quantum numbers corresponding to isotopic spin and to 'strangeness'; one consequences is that, at least in elementary interactions, charge is only conserved module 4. Furthermore, particle states have not a well-defined parity, but parity is effectively conserved for meson-nucleon interactions. A simplified model, using only two dimensions of space and iso-space, is considered further; the non-linear meson field has solutions with particle character, and an indication is given of the way in which the particle field variables might be introduced as collective co-ordinates describing the dynamics of these particular solutions of the meson field equations, suggesting a unified theory based on the meson field alone. (author). 7 refs
A Theory for the Incubation Period Following a Stress Reduction During Creep
DEFF Research Database (Denmark)
Bilde-Sørensen, Jørgen
1978-01-01
incubation period is much shorter than the time needed to establish an equilibrium structure at the new lower stress. The dependence of dislocation line tension upon line length is taken into account; as a result of this, recovery rates are predicted to depend on stress to a power larger than three......A dislocation model is presented for the phenomena following a stress reduction during creep. It is suggested that an incubation period for the production of new mobile dislocations arises because attractive junctions on the verge of breaking just before the stress reduction are no longer so after...... the stress reduction. The breaking stress of the junctions must be lowered by climb movements in the surrounding network before the junctions can break and release new mobile dislocations. On the basis of these concepts, an expression is derived for the length of the incubation period. This theoretical...
Nonlinear polarization of ionic liquids: theory, simulations, experiments
Kornyshev, Alexei
2010-03-01
Room temperature ionic liquids (RTILs) composed of large, often asymmetric, organic cations and simple or complex inorganic or organic anions do not freeze at ambient temperatures. Their rediscovery some 15 years ago is widely accepted as a ``green revolution'' in chemistry, offering an unlimited number of ``designer'' solvents for chemical and photochemical reactions, homogeneous catalysis, lubrication, and solvent-free electrolytes for energy generation and storage. As electrolytes they are non-volatile, some can sustain without decomposition up to 6 times higher voltages than aqueous electrolytes, and many are environmentally friendly. The studies of RTILs and their applications have reached a critical stage. So many of them can be synthesized - about a thousand are known already - their mixtures can further provide ``unlimited'' number of combinations! Thus, establishing some general laws that could direct the best choice of a RTIL for a given application became crucial; guidance is expected from theory and modelling. But for a physical theory, RTILs comprise a peculiar and complex class of media, the description of which lies at the frontier line of condensed matter theoretical physics: dense room temperature ionic plasmas with ``super-strong'' Coulomb correlations, which behave like glasses at short time-scale, but like viscous liquids at long-time scale. This talk will introduce RTILs to physicists and overview the current understanding of the nonlinear response of RTILs to electric field. It will focus on the theory, simulations, and experimental characterisation of the structure and nonlinear capacitance of the electrical double layer at a charged electrode. It will also discuss pros and contras of supercapacitor applications of RTILs.
Linear theory for filtering nonlinear multiscale systems with model error.
Berry, Tyrus; Harlim, John
2014-07-08
In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online , as part of a filtering
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
Plasticity and creep of metals
Rusinko, Andrew
2011-01-01
Here is a systematic presentation of the postulates, theorems and principles of mathematical theories of plasticity and creep in metals, and their applications. Special attention is paid to analysis of the advantages and shortcomings of the classical theories.
Theory of weakly nonlinear self-sustained detonations
Faria, Luiz
2015-11-03
We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced unsteady small-disturbance transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multidimensional detonations.
Nonlinear problems of the theory of heterogeneous slightly curved shells
Kantor, B. Y.
1973-01-01
An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.
History of nonlinear oscillations theory in France (1880-1940)
Ginoux, Jean-Marc
2017-01-01
This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars. Readers will see that, contrary to what is often written, France's role has been significant. Important contributions were made through both the work of French scholars from within diverse disciplines (mathematicians, physicists, engineers), and through the geographical crossroads that France provided to scientific communication at the time. This study includes an examination of the period before the First World War which is vital to understanding the work of the later period. By examining literature sources such as periodicals on the topic of electricity from that era, the author has unearthed a very important text by Henri Poincaré, dating from 1908. In this work Poincaré applied the concept of limit cycle (which he had introduced in 1882 through his own...
Finite Element Modeling of Thermo Creep Processes Using Runge-Kutta Method
Directory of Open Access Journals (Sweden)
Yu. I. Dimitrienko
2015-01-01
Full Text Available Thermo creep deformations for most heat-resistant alloys, as a rule, nonlinearly depend on stresses and are practically non- reversible. Therefore, to calculate the properties of these materials the theory of plastic flow is most widely used. Finite-element computations of a stress-strain state of structures with account of thermo creep deformations up to now are performed using main commercial software, including ANSYS package. However, in most cases to solve nonlinear creep equations, one should apply explicit or implicit methods based on the Euler method of approximation of time-derivatives. The Euler method is sufficiently efficient in terms of random access memory in computations, however this method is cumbersome in computation time and does not always provide a required accuracy for creep deformation computations.The paper offers a finite-element algorithm to solve a three-dimensional problem of thermo creep based on the Runge-Kutta finite-difference schemes of different orders with respect to time. It shows a numerical test example to solve the problem on the thermo creep of a beam under tensile loading. The computed results demonstrate that using the Runge-Kutta method with increasing accuracy order allows us to obtain a more accurate solution (with increasing accuracy order by 1 a relative error decreases, approximately, by an order too. The developed algorithm proves to be efficient enough and can be recommended for solving the more complicated problems of thermo creep of structures.
A general theory of two-wave mixing in nonlinear media
DEFF Research Database (Denmark)
Chi, Mingjun; Huignard, Jean-Pierre; Petersen, Paul Michael
2009-01-01
A general theory of two-wave mixing in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave e...
Nonlinear theory of the collisional Rayleigh-Taylor instability in equatorial spread F
International Nuclear Information System (INIS)
Chaturvedi, P.K.; Ossakow, S.L.
1977-01-01
The nonlinear behavior of the collisional Rayleigh-Taylor instability is studied in equatorial Spread F by including a dominant two-dimensional nonlinearity. It is found that on account of this nonlinearity the instability saturates by generating damped higher spatial harmonics. The saturated power spectrum for the density fluctuations is discussed. A comparison between experimental observations and theory is presented
Tensile cracks in creeping solids
International Nuclear Information System (INIS)
Riedel, H.; Rice, J.R.
1979-02-01
The loading parameter determining the stress and strain fields near a crack tip, and thereby the growth of the crack, under creep conditions is discussed. Relevant loading parameters considered are the stress intensity factor K/sub I/, the path-independent integral C*, and the net section stress sigma/sub net/. The material behavior is modelled as elastic-nonlinear viscous where the nonlinear term describes power law creep. At the time t = 0 load is applied to the cracked specimen, and in the first instant the stress distribution is elastic. Subsequently, creep deformation relaxes the initial stress concentration at the crack tip, and creep strains develop rapidly near the crack tip. These processes may be analytically described by self-similar solutions for short times t. Small scale yielding may be defined. In creep problems, this means that elastic strains dominate almost everywhere except in a small creep zone which grows around the crack tip. If crack growth ensues while the creep zone is still small compared with the crack length and the specimen size, the stress intensity factor governs crack growth behavior. If the calculated creep zone becomes larger than the specimen size, the stresses become finally time-independent and the elastic strain rates can be neglected. In this case, the stress field is the same as in the fully-plastic limit of power law hardening plasticity. The loading parameter which determines the near tip fields uniquely is then the path-independent integral C*.K/sub I/ and C* characterize opposite limiting cases. The case applied in a given situation is decided by comparing the creep zone size with the specimen size and the crack length. Besides several methods of estimating the creep zone size, a convenient expression for a characteristic time is derived, which characterizes the transition from small scale yielding to extensive creep of the whole specimen
Creep model of unsaturated sliding zone soils and long-term deformation analysis of landslides
Zou, Liangchao; Wang, Shimei; Zhang, Yeming
2015-04-01
Sliding zone soil is a special soil layer formed in the development of a landslide. Its creep behavior plays a significant role in long-term deformation of landslides. Due to rainfall infiltration and reservoir water level fluctuation, the soils in the slide zone are often in unsaturated state. Therefore, the investigation of creep behaviors of the unsaturated sliding zone soils is of great importance for understanding the mechanism of the long-term deformation of a landslide in reservoir areas. In this study, the full-process creep curves of the unsaturated soils in the sliding zone in different net confining pressure, matric suctions and stress levels were obtained from a large number of laboratory triaxial creep tests. A nonlinear creep model for unsaturated soils and its three-dimensional form was then deduced based on the component model theory and unsaturated soil mechanics. This creep model was validated with laboratory creep data. The results show that this creep model can effectively and accurately describe the nonlinear creep behaviors of the unsaturated sliding zone soils. In order to apply this creep model to predict the long-term deformation process of landslides, a numerical model for simulating the coupled seepage and creep deformation of unsaturated sliding zone soils was developed based on this creep model through the finite element method (FEM). By using this numerical model, we simulated the deformation process of the Shuping landslide located in the Three Gorges reservoir area, under the cycling reservoir water level fluctuation during one year. The simulation results of creep displacement were then compared with the field deformation monitoring data, showing a good agreement in trend. The results show that the creeping deformations of landslides have strong connections with the changes of reservoir water level. The creep model of unsaturated sliding zone soils and the findings obtained by numerical simulations in this study are conducive to
Creep cavitation effects in polycrystalline alumina
International Nuclear Information System (INIS)
Porter, J.R.; Blumenthal, W.; Evans, A.G.
1981-01-01
Fine grained polycrystalline alumina has been deformed in creep at high temperatures, to examine the evolution of cavities at grain boundaries. Cavities with equilibrium and crack-like morphologies have been observed, distributed nonuniformly throughout the material. The role of these cavities during creep has been described. A transition from equilibrium to crack-like morphology has been observed and correlated with a model based on the influence of the surface to boundary diffusivity ratio and the local tensile stress. The contribution of cavitation to the creep rate and total creep strain has been analyzed and excluded as the principal cause of the observed non-linear creep rate
Non-linearities in Theory-of-Mind Development.
Blijd-Hoogewys, Els M A; van Geert, Paul L C
2016-01-01
Research on Theory-of-Mind (ToM) has mainly focused on ages of core ToM development. This article follows a quantitative approach focusing on the level of ToM understanding on a measurement scale, the ToM Storybooks, in 324 typically developing children between 3 and 11 years of age. It deals with the eventual occurrence of developmental non-linearities in ToM functioning, using smoothing techniques, dynamic growth model building and additional indicators, namely moving skewness, moving growth rate changes and moving variability. The ToM sum-scores showed an overall developmental trend that leveled off toward the age of 10 years. Within this overall trend two non-linearities in the group-based change pattern were found: a plateau at the age of around 56 months and a dip at the age of 72-78 months. These temporary regressions in ToM sum-score were accompanied by a decrease in growth rate and variability, and a change in skewness of the ToM data, all suggesting a developmental shift in ToM understanding. The temporary decreases also occurred in the different ToM sub-scores and most clearly so in the core ToM component of beliefs. It was also found that girls had an earlier growth spurt than boys and that the underlying developmental path was more salient in girls than in boys. The consequences of these findings are discussed from various theoretical points of view, with an emphasis on a dynamic systems interpretation of the underlying developmental paths.
Transmission Creep: Media Effects Theories and Journalism Studies in a Digital Era
Singer, J.
2016-01-01
The nature of digital media challenges the explanatory power of effects theories that rest on a transmission model of communication. As essentially linear conceptualizations reliant on identification and measurement of discrete message components, these twentieth-century theories are poorly suited to contemporary journalistic structures and forms. This article adds to the call for a more richly theorized concept of relationship effects suitable to an immersive, iterative, and interconnected e...
Assessment of an improved multiaxial strength theory based on creep-rupture data for Inconel 600
International Nuclear Information System (INIS)
Huddleston, R.L.
1993-01-01
A new multiaxial strength theory incorporating three independent stress parameters was developed and reported by the author in 1984. It was formally incorporated into ASME Code Case N47-29 in 1990. The new theory provided significantly more accurate stress-rupture life predictions than obtained using the classical theories of von Mises, Tresca, and Rankins (maximum principal stress), for Types 304 and 316 stainless steel tested at 593 and 600 degrees C respectively under different biaxial stress states. Additional results for Inconel 600 specimens tested at 816 degrees C under tension-tension and tension-compression stress states are presented in this paper and show a factor of approximately 2.4 reduction in the scatter of predicted versus observed lives as compared to the classical theories of von Mises and Tresca and a factor of about 5 as compared to the Rankins theory. A key feature of the theory, which incorporates the maximum deviatoric stress, the first invariant of the stress tensor, and the second invariant of the deviatoric stress tensor, is its ability to distinguish between life under tensile versus compressive stress states
Dai, Gaole; Shang, Jin; Huang, Jiping
2018-02-01
Heat can transfer via thermal conduction, thermal radiation, and thermal convection. All the existing theories of transformation thermotics and optics can treat thermal conduction and thermal radiation, respectively. Unfortunately, thermal convection has seldom been touched in transformation theories due to the lack of a suitable theory, thus limiting applications associated with heat transfer through fluids (liquid or gas). Here, we develop a theory of transformation thermal convection by considering the convection-diffusion equation, the equation of continuity, and the Darcy law. By introducing porous media, we get a set of equations keeping their forms under coordinate transformation. As model applications, the theory helps to show the effects of cloaking, concentrating, and camouflage. Our finite-element simulations confirm the theoretical findings. This work offers a transformation theory for thermal convection, thus revealing novel behaviors associated with potential applications; it not only provides different hints on how to control heat transfer by combining thermal conduction, thermal convection, and thermal radiation, but also benefits mass diffusion and other related fields that contain a set of equations and need to transform velocities at the same time.
Janus field theories from non-linear BF theories for multiple M2-branes
International Nuclear Information System (INIS)
Ryang, Shijong
2009-01-01
We integrate the nonpropagating B μ gauge field for the non-linear BF Lagrangian describing N M2-branes which includes terms with even number of the totally antisymmetric tensor M IJK in arXiv:0808.2473 and for the two-types of non-linear BF Lagrangians which include terms with odd number of M IJK as well in arXiv:0809:0985. For the former Lagrangian we derive directly the DBI-type Lagrangian expressed by the SU(N) dynamical A μ gauge field with a spacetime dependent coupling constant, while for the low-energy expansions of the latter Lagrangians the B μ integration is iteratively performed. The derived Janus field theory Lagrangians are compared.
Transient response of nonlinear polymer networks: A kinetic theory
Vernerey, Franck J.
2018-06-01
Dynamic networks are found in a majority of natural materials, but also in engineering materials, such as entangled polymers and physically cross-linked gels. Owing to their transient bond dynamics, these networks display a rich class of behaviors, from elasticity, rheology, self-healing, or growth. Although classical theories in rheology and mechanics have enabled us to characterize these materials, there is still a gap in our understanding on how individuals (i.e., the mechanics of each building blocks and its connection with others) affect the emerging response of the network. In this work, we introduce an alternative way to think about these networks from a statistical point of view. More specifically, a network is seen as a collection of individual polymer chains connected by weak bonds that can associate and dissociate over time. From the knowledge of these individual chains (elasticity, transient attachment, and detachment events), we construct a statistical description of the population and derive an evolution equation of their distribution based on applied deformation and their local interactions. We specifically concentrate on nonlinear elastic response that follows from the strain stiffening response of individual chains of finite size. Upon appropriate averaging operations and using a mean field approximation, we show that the distribution can be replaced by a so-called chain distribution tensor that is used to determine important macroscopic measures such as stress, energy storage and dissipation in the network. Prediction of the kinetic theory are then explored against known experimental measurement of polymer responses under uniaxial loading. It is found that even under the simplest assumptions of force-independent chain kinetics, the model is able to reproduce complex time-dependent behaviors of rubber and self-healing supramolecular polymers.
Quantum theory of a one-dimensional laser with output coupling. 2. Nonlinear theory
International Nuclear Information System (INIS)
Penaforte, J.C.; Baseia, B.
1984-01-01
A previous paper describing the quantum theory of a laser in linear approximation is here extended to the nonlinear case. Instead of the approach of conventional theory - which deals with discrete 'cavity-modes' and includes artificial mechanisms to simulates radiation field losses due to beam extraction - a more realistic model of optical cavity having output coupling is used that works entirely within the continuous spectrum, allowing one to obtain the equations for the field both inside and outside the laser cavity. Besides the quantum noise due to spontaneous emission, a noise term of classical nature due to transmission losses automatically emerges from the present treatment. For single-collective-mode operation the equations for laser field are solved exactly, yielding the transient and steady-state solutions. Inside the laser cavity, the results of nonlinear analysis agree with those found in conventional theory once the conventional 'mode-amplitude' is reinterpreted as a collective variable. Outside the cavity - unaccessible region in the conventional treatment - the solution for the laser field is also exhibited. Further considerations as concerning the role played by the noise terms in the field buildup are discussed. (Author) [pt
Microscopic theory of linear and nonlinear terahertz spectroscopy of semiconductors
Energy Technology Data Exchange (ETDEWEB)
Steiner, Johannes
2008-12-09
This Thesis presents a fully microscopic theory to describe terahertz (THz)-induced processes in optically-excited semiconductors. The formation process of excitons and other quasi-particles after optical excitation has been studied in great detail for a variety of conditions. Here, the formation process is not modelled but a realistic initial many-body state is assumed. In particular, the linear THz response is reviewed and it is demonstrated that correlated quasi-particles such as excitons and plasmons can be unambiguously detected via THz spectroscopy. The focus of the investigations, however, is on situations where the optically-excited many-body state is excited by intense THz fields. While weak pulses detect the many-body state, strong THz pulses control and manipulate the quasi-particles in a way that is not accessible via conventional techniques. The nonlinear THz dynamics of exciton populations is especially interesting because similarities and differences to optics with atomic systems can be studied. (orig.)
Creep buckling analysis of shells
International Nuclear Information System (INIS)
Stone, C.M.; Nickell, R.E.
1977-01-01
The current study was conducted in an effort to determine the degree of conservatism or lack of conservatism in current ASME design rules concerning time-dependent (creep) buckling. In the course of this investigation, certain observations were made concerning the numerical solution of creep buckling problems. It was demonstrated that a nonlinear finite element code could be used to solve the time-dependent buckling problem. A direct method of solution was presented which proved to be computationally efficient and provided answers which agreed very well with available analytical solutions. It was observed that the calculated buckling times could vary widely for small errors in computed displacements. The presence of high creep strain rates contributed to the prediction of early buckling times when calculated during the primary creep stage. The predicted time estimates were found to increase with time until the secondary stage was reached and the estimates approached the critical times predicted without primary creep. It can be concluded, therefore, that for most nuclear piping components, whose primary creep stage is small compared to the secondary stage, the effect of primary creep is negligible and can be omitted from the calculations. In an evaluation of the past and current ASME design rules for time-dependent, load controlled buckling, it was concluded that current use of design load safety factors is not equivalent to a safety factor of ten on service life for low creep exponents
Explicit Nonlinear Model Predictive Control Theory and Applications
Grancharova, Alexandra
2012-01-01
Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...
Untangling the drivers of nonlinear systems with information theory
Wing, S.; Johnson, J.
2017-12-01
Many systems found in nature are nonlinear. The drivers of the system are often nonlinearly correlated with one another, which makes it a challenge to understand the effects of an individual driver. For example, solar wind velocity (Vsw) and density (nsw) are both found to correlate well with radiation belt fluxes and are thought to be drivers of the magnetospheric dynamics; however, the Vsw is anti-correlated with nsw, which can potentially confuse interpretation of these relationships as causal or coincidental. Information theory can untangle the drivers of these systems, describe the underlying dynamics, and offer constraints to modelers and theorists, leading to better understanding of the systems. Two examples are presented. In the first example, the solar wind drivers of geosynchronous electrons with energy range of 1.8-3.5 MeV are investigated using mutual information (MI), conditional mutual information (CMI), and transfer entropy (TE). The information transfer from Vsw to geosynchronous MeV electron flux (Je) peaks with a lag time (t) of 2 days. As previously reported, Je is anticorrelated with nsw with a lag of 1 day. However, this lag time and anticorrelation can be attributed mainly to the Je(t + 2 days) correlation with Vsw(t) and nsw(t + 1 day) anticorrelation with Vsw(t). Analyses of solar wind driving of the magnetosphere need to consider the large lag times, up to 3 days, in the (Vsw, nsw) anticorrelation. Using CMI to remove the effects of Vsw, the response of Je to nsw is 30% smaller and has a lag time < 24 hr, suggesting that the loss mechanism due to nsw or solar wind dynamic pressure has to start operating in < 24 hr. nsw transfers about 36% as much information as Vsw (the primary driver) to Je. Nonstationarity in the system dynamics are investigated using windowed TE. When the data is ordered according to high or low transfer entropy it is possible to understand details of the triangle distribution that has been identified between Je(t + 2
Nonlinear theory of scattering by localized potentials in metals
Energy Technology Data Exchange (ETDEWEB)
Howard, I A [Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp (Belgium); March, N H [Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp (Belgium); Oxford University, Oxford (United Kingdom); Echenique, P M [Donostia International Physics Center (DIPC), 20018 San Sebastian, Basque Country (Spain); Departamento de Fisica de Materiales and Centro Mixto CSIC-UPV/EHU, Facultad de Quimicas, UPV/EHU, Apartado 1072, 20080, San Sebastian (Spain)
2003-11-14
In early work, March and Murray gave a perturbation theory of the Dirac density matrix {gamma}(r, r') generated by a localized potential V(r) embedded in an initially uniform Fermi gas to all orders in V(r). For potentials sufficiently slowly varying in space, they summed the resulting series for r' = r to regain the Thomas-Fermi density {rho}(r) {proportional_to} [{mu} - V(r)]{sup 3/2}, with {mu} the chemical potential of the Fermi gas. For an admittedly simplistic repulsive central potential V(r) = vertical bar A vertical bar exp(-cr), it is first shown here that what amounts to the sum of the March-Murray series for the s-wave (only) contribution to the density, namely {rho}{sub s}(r, {mu}), can be obtained in closed form. Furthermore, for specific numerical values of A and c in this exponential potential, the long-range behaviour of {rho}{sub s}(r, {mu}) is related to the zero-potential form of March and Murray, which merely suffers a {mu}-dependent phase shift. This result is interpreted in relation to the recent high density screening theorem of Zaremba, Nagy and Echenique. A brief discussion of excess electrical resistivity caused by nonlinear scattering in a Fermi gas is added; this now involves an off-diagonal local density of states. Finally, for periodic lattices, contact is made with the quantum-mechanical defect centre models of Koster and Slater (1954 Phys. Rev. 96 1208) and of Beeby (1967 Proc. R. Soc. A 302 113), and also with the semiclassical approximation of Friedel (1954 Adv. Phys. 3 446). In appendices, solvable low-dimensional models are briefly summarized.
Robust methods and asymptotic theory in nonlinear econometrics
Bierens, Herman J
1981-01-01
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...
Theory of Nonlinear Dispersive Waves and Selection of the Ground State
International Nuclear Information System (INIS)
Soffer, A.; Weinstein, M.I.
2005-01-01
A theory of time-dependent nonlinear dispersive equations of the Schroedinger or Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear master equations (NLME), governing the evolution of the mode powers, and by a novel multitime scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include Bose-Einstein condensate large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, 'selection of the ground state', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et al. in nonlinear optical waveguides
Origin of soft limits from nonlinear supersymmetry in Volkov-Akulov theory
Energy Technology Data Exchange (ETDEWEB)
Kallosh, Renata; Karlsson, Anna; Murli, Divyanshu [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94305 (United States)
2017-03-15
We apply the background field technique, recently developed for a general class of nonlinear symmetries, at tree level, to the Volkov-Akulov theory with spontaneously broken N=1 supersymmetry. We find that the background field expansion in terms of the free fields to the lowest order reproduces the nonlinear supersymmetry transformation rules. The double soft limit of the background field is, in agreement with the new general identities, defined by the algebra of the nonlinear symmetries.
Geometrical phases from global gauge invariance of nonlinear classical field theories
International Nuclear Information System (INIS)
Garrison, J.C.; Chiao, R.Y.
1988-01-01
We show that the geometrical phases recently discovered in quantum mechanics also occur naturally in the theory of any classical complex multicomponent field satisfying nonlinear equations derived from a Lagrangean with is invariant under gauge transformations of the first kind. Some examples are the paraxial wave equation for nonlinear optics, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics
Nanogranular origin of concrete creep.
Vandamme, Matthieu; Ulm, Franz-Josef
2009-06-30
Concrete, the solid that forms at room temperature from mixing Portland cement with water, sand, and aggregates, suffers from time-dependent deformation under load. This creep occurs at a rate that deteriorates the durability and truncates the lifespan of concrete structures. However, despite decades of research, the origin of concrete creep remains unknown. Here, we measure the in situ creep behavior of calcium-silicate-hydrates (C-S-H), the nano-meter sized particles that form the fundamental building block of Portland cement concrete. We show that C-S-H exhibits a logarithmic creep that depends only on the packing of 3 structurally distinct but compositionally similar C-S-H forms: low density, high density, ultra-high density. We demonstrate that the creep rate ( approximately 1/t) is likely due to the rearrangement of nanoscale particles around limit packing densities following the free-volume dynamics theory of granular physics. These findings could lead to a new basis for nanoengineering concrete materials and structures with minimal creep rates monitored by packing density distributions of nanoscale particles, and predicted by nanoscale creep measurements in some minute time, which are as exact as macroscopic creep tests carried out over years.
Sensitivity theory for general non-linear algebraic equations with constraints
International Nuclear Information System (INIS)
Oblow, E.M.
1977-04-01
Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems
An Asymptotic Derivation of Weakly Nonlinear Ray Theory
Indian Academy of Sciences (India)
The transport equation for the amplitude has been deduced with an error (2) where is the small parameter appearing in the high frequency approximation. On a length scale over which Choquet–Bruhat's theory is valid, this theory reduces to the former. The theory is valid on a much larger length scale and the leading ...
Non-linear σ-models and string theories
International Nuclear Information System (INIS)
Sen, A.
1986-10-01
The connection between σ-models and string theories is discussed, as well as how the σ-models can be used as tools to prove various results in string theories. Closed bosonic string theory in the light cone gauge is very briefly introduced. Then, closed bosonic string theory in the presence of massless background fields is discussed. The light cone gauge is used, and it is shown that in order to obtain a Lorentz invariant theory, the string theory in the presence of background fields must be described by a two-dimensional conformally invariant theory. The resulting constraints on the background fields are found to be the equations of motion of the string theory. The analysis is extended to the case of the heterotic string theory and the superstring theory in the presence of the massless background fields. It is then shown how to use these results to obtain nontrivial solutions to the string field equations. Another application of these results is shown, namely to prove that the effective cosmological constant after compactification vanishes as a consequence of the classical equations of motion of the string theory. 34 refs
Symmetry properties of some nonlinear field theory models
International Nuclear Information System (INIS)
Shvachka, A.B.
1984-01-01
Various approaches towards the study of symmetry properties of some nonlinear evolution equations as well as possible ways of their computer implementation using the computer algebra systems langage are discussed. Special attention is paid to the method of pseudopotential investigation of formal integrability and isovector method for the equations of balance
Nonlinear theory of diffusive acceleration of particles by shock waves
Energy Technology Data Exchange (ETDEWEB)
Malkov, M.A. [University of California at San Diego, La Jolla, CA (United States)]. E-mail: mmalkov@ucsd.edu; Drury, L. O' C. [Dublin Institute for Advanced Studies, 5 Merrion Square, Dublin 2 (Ireland)
2001-04-01
Among the various acceleration mechanisms which have been suggested as responsible for the nonthermal particle spectra and associated radiation observed in many astrophysical and space physics environments, diffusive shock acceleration appears to be the most successful. We review the current theoretical understanding of this process, from the basic ideas of how a shock energizes a few reactionless particles to the advanced nonlinear approaches treating the shock and accelerated particles as a symbiotic self-organizing system. By means of direct solution of the nonlinear problem we set the limit to the test-particle approximation and demonstrate the fundamental role of nonlinearity in shocks of astrophysical size and lifetime. We study the bifurcation of this system, proceeding from the hydrodynamic to kinetic description under a realistic condition of Bohm diffusivity. We emphasize the importance of collective plasma phenomena for the global flow structure and acceleration efficiency by considering the injection process, an initial stage of acceleration and, the related aspects of the physics of collisionless shocks. We calculate the injection rate for different shock parameters and different species. This, together with differential acceleration resulting from nonlinear large-scale modification, determines the chemical composition of accelerated particles. The review concentrates on theoretical and analytical aspects but our strategic goal is to link the fundamental theoretical ideas with the rapidly growing wealth of observational data. (author)
Strongly nonlinear theory of rapid solidification near absolute stability
Kowal, Katarzyna N.; Altieri, Anthony L.; Davis, Stephen H.
2017-10-01
We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise. In contrast to the morphological stability problem in equilibrium, in which only cellular instabilities appear and only one absolute stability boundary exists, in disequilibrium the system is prone to oscillatory instabilities and a second absolute stability boundary involving attachment kinetics arises. Large enough attachment kinetics stabilize the oscillatory instabilities. We derive a nonlinear evolution equation to describe the nonlinear development of the solid-liquid interface near this oscillatory absolute stability limit. We find that strong asymmetries develop with time. For uniform oscillations, the evolution equation for the interface reduces to the simple form f''+(βf')2+f =0 , where β is the disequilibrium parameter. Lastly, we investigate a distinguished limit near both absolute stability limits in which the system is prone to both cellular and oscillatory instabilities and derive a nonlinear evolution equation that captures the nonlinear deformations in this limit. Common to all these scenarios is the emergence of larger asymmetries in the resulting shapes of the solid-liquid interface with greater departures from equilibrium and larger morphological numbers. The disturbances additionally sharpen near the oscillatory absolute stability boundary, where the interface becomes deep-rooted. The oscillations are time-periodic only for small-enough initial amplitudes and their frequency depends on a single combination of physical parameters, including the
Complexity, Chaos, and Nonlinear Dynamics: A New Perspective on Career Development Theory
Bloch, Deborah P.
2005-01-01
The author presents a theory of career development drawing on nonlinear dynamics and chaos and complexity theories. Career is presented as a complex adaptive entity, a fractal of the human entity. Characteristics of complex adaptive entities, including (a) autopiesis, or self-regeneration; (b) open exchange; (c) participation in networks; (d)…
Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
. Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...
A nonlinear theory for elastic plates with application to characterizing paper properties
M. W. Johnson; Thomas J. Urbanik
1984-03-01
A theory of thin plates which is physically as well as kinematically nonlinear is, developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a...
Silva, Walter A.
1993-01-01
A methodology for modeling nonlinear unsteady aerodynamic responses, for subsequent use in aeroservoelastic analysis and design, using the Volterra-Wiener theory of nonlinear systems is presented. The methodology is extended to predict nonlinear unsteady aerodynamic responses of arbitrary frequency. The Volterra-Wiener theory uses multidimensional convolution integrals to predict the response of nonlinear systems to arbitrary inputs. The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code is used to generate linear and nonlinear unit impulse responses that correspond to each of the integrals for a rectangular wing with a NACA 0012 section with pitch and plunge degrees of freedom. The computed kernels then are used to predict linear and nonlinear unsteady aerodynamic responses via convolution and compared to responses obtained using the CAP-TSD code directly. The results indicate that the approach can be used to predict linear unsteady aerodynamic responses exactly for any input amplitude or frequency at a significant cost savings. Convolution of the nonlinear terms results in nonlinear unsteady aerodynamic responses that compare reasonably well with those computed using the CAP-TSD code directly but at significant computational cost savings.
Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory
DEFF Research Database (Denmark)
Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav
model is presented in the form of partial differential equations (PDE). Galerkin's method is then applied to obtain a set of ordinary differential equations such that the cable model is approximated by a FEM model. Based on the FEM model, a nonlinear observer is designed to estimate the cable...
New solutions of a nonlinear classical field theory
International Nuclear Information System (INIS)
Marques, G.C.; Ventura, I.
1975-01-01
New solutions of a relativistic, classical, field theoretical model having logarithmic nonlinearities are obtained. Some of these solutions correspond to field not bounded in time but having finite energy and charge. There are no bounded solutions (bound states and resonances in particular) if the charge exceeds a certain value. This effect is due to the existance of a 'charge barrier' in this field theoretical model. All calculations are performed in a number of spatial dimensions [pt
Nonlinear time series theory, methods and applications with R examples
Douc, Randal; Stoffer, David
2014-01-01
FOUNDATIONSLinear ModelsStochastic Processes The Covariance World Linear Processes The Multivariate Cases Numerical Examples ExercisesLinear Gaussian State Space Models Model Basics Filtering, Smoothing, and Forecasting Maximum Likelihood Estimation Smoothing Splines and the Kalman Smoother Asymptotic Distribution of the MLE Missing Data Modifications Structural Component Models State-Space Models with Correlated Errors Exercises Beyond Linear ModelsNonlinear Non-Gaussian Data Volterra Series Expansion Cumulants and Higher-Order Spectra Bilinear Models Conditionally Heteroscedastic Models Thre
International Nuclear Information System (INIS)
Doering, C.R.
1985-01-01
Applications of nonlinear parabolic stochastic differential equations with additive colored noise in equilibrium and nonequilibrium statistical mechanics and quantum field theory are developed in detail, providing a new unified mathematical approach to many problems. The existence and uniqueness of solutions to these equations is established, and some of the properties of the solutions are investigated. In particular, asymptotic expansions for the correlation functions of the solutions are introduced and compared to rigorous nonperturbative bounds on the moments. It is found that the perturbative analysis is in qualitative disagreement with the exact result in models corresponding to cut-off self-interacting nonperturbatively renormalizable scalar quantum field theories. For these theories the nonlinearities cannot be considered as perturbations of the linearized theory
Lattice continuum and diffusional creep.
Mesarovic, Sinisa Dj
2016-04-01
Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro-Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro-Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.
Quantization of a non-linearly realized supersymmetric theory
International Nuclear Information System (INIS)
Shima, Kazunari
1976-01-01
The two-dimensional version of the Volkov-Akulov's Lagrngian, where the super-symmetry is realized non-linearly by means of a single Majorana spinor psi(x), is quantized. The equal time anti-commutators for the field are not c-numbers but functions of the field itself. By the explicite calculation we shall show that supersymmetry charges of the model form the supersymmetry algebra(the graded Lie algebra) and the supersymmetry charges exactly generate a constant translation of psi(x) in the spinor space. In this work we restrict our investigation to the two-dimensional space-time for the sake of simplicity. (auth.)
Nonlinear Theory of Nonparaxial Laser Pulse Propagation in Plasma Channels
International Nuclear Information System (INIS)
Esarey, E.; Schroeder, C. B.; Shadwick, B. A.; Wurtele, J. S.; Leemans, W. P.
2000-01-01
Nonparaxial propagation of ultrashort, high-power laser pulses in plasma channels is examined. In the adiabatic limit, pulse energy conservation, nonlinear group velocity, damped betatron oscillations, self-steepening, self-phase modulation, and shock formation are analyzed. In the nonadiabatic limit, the coupling of forward Raman scattering (FRS) and the self-modulation instability (SMI) is analyzed and growth rates are derived, including regimes of reduced growth. The SMI is found to dominate FRS in most regimes of interest. (c) 2000 The American Physical Society
Nonlinear theory of transverse-multimode plasma accelerators
International Nuclear Information System (INIS)
Kuzelev, M.V.; Panin, V.A.; Plotnikov, A.P.
1991-01-01
The excitation of the higher transverse modes in a plasma-filled waveguide by a high-power electron beam is considered. General nonlinear equations are obtained which treat the excitation of the higher transverse plasma waves by a high-current relativistic beam. Results are presented of the numerical solutions of these equations. In the case of ultrarelativistic beams analytical expressions are found for the maximum amplitudes of the excited modes and the Q of the amplification. Numerical estimates are presented for realistic parameters
Beyond the SM with nonlinearly realized gauge theories
International Nuclear Information System (INIS)
ERRARI, R.
2014-01-01
A Stuckelberg Mass Term (SMT) is introduced in a SU(2) non-abelian gauge theory as an alternative to the Higgs mechanism. A lattice model is used in order to investigate the mass spectrum of the theory, in particular the presence of Higgs-like bound states. Simulations indicate the presence of neutral bound states. Further investigations are needed in order to compare the model with experiments.
Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory
Bridges, Thomas J.; Ratliff, Daniel J.
2018-04-01
The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Boussinesq equation. This equation is universal in the same sense as Whitham theory. Moreover, it is dispersive, and it has a wide range of interesting multi-periodic, quasi-periodic and multi-pulse localized solutions. For illustration the theory is applied to a complex nonlinear 2+1 Klein-Gordon equation which has two Lighthill surfaces in the manifold of periodic travelling waves. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.
Durning, Steven J; Lubarsky, Stuart; Torre, Dario; Dory, Valérie; Holmboe, Eric
2015-01-01
The purpose of this article is to propose new approaches to assessment that are grounded in educational theory and the concept of "nonlinearity." The new approaches take into account related phenomena such as "uncertainty," "ambiguity," and "chaos." To illustrate these approaches, we will use the example of assessment of clinical reasoning, although the principles we outline may apply equally well to assessment of other constructs in medical education. Theoretical perspectives include a discussion of script theory, assimilation theory, self-regulated learning theory, and situated cognition. Assessment examples to include script concordance testing, concept maps, self-regulated learning microanalytic technique, and work-based assessment, which parallel the above-stated theories, respectively, are also highlighted. We conclude with some practical suggestions for approaching nonlinearity. © 2015 The Alliance for Continuing Education in the Health Professions, the Society for Academic Continuing Medical Education, and the Council on Continuing Medical Education, Association for Hospital Medical Education.
Nonlinear Dynamic Theory of Acute Cell Injuries and Brain Ischemia
Taha, Doaa; Anggraini, Fika; Degracia, Donald; Huang, Zhi-Feng
2015-03-01
Cerebral ischemia in the form of stroke and cardiac arrest brain damage affect over 1 million people per year in the USA alone. In spite of close to 200 clinical trials and decades of research, there are no treatments to stop post-ischemic neuron death. We have argued that a major weakness of current brain ischemia research is lack of a deductive theoretical framework of acute cell injury to guide empirical studies. A previously published autonomous model based on the concept of nonlinear dynamic network was shown to capture important facets of cell injury, linking the concept of therapeutic to bistable dynamics. Here we present an improved, non-autonomous formulation of the nonlinear dynamic model of cell injury that allows multiple acute injuries over time, thereby allowing simulations of both therapeutic treatment and preconditioning. Our results are connected to the experimental data of gene expression and proteomics of neuron cells. Importantly, this new model may be construed as a novel approach to pharmacodynamics of acute cell injury. The model makes explicit that any pro-survival therapy is always a form of sub-lethal injury. This insight is expected to widely influence treatment of acute injury conditions that have defied successful treatment to date. This work is supported by NIH NINDS (NS081347) and Wayne State University President's Research Enhancement Award.
Nonlinear spectral mixing theory to model multispectral signatures
Energy Technology Data Exchange (ETDEWEB)
Borel, C.C. [Los Alamos National Lab., NM (United States). Astrophysics and Radiation Measurements Group
1996-02-01
Nonlinear spectral mixing occurs due to multiple reflections and transmissions between discrete surfaces, e.g. leaves or facets of a rough surface. The radiosity method is an energy conserving computational method used in thermal engineering and it models nonlinear spectral mixing realistically and accurately. In contrast to the radiative transfer method the radiosity method takes into account the discreteness of the scattering surfaces (e.g. exact location, orientation and shape) such as leaves and includes mutual shading between them. An analytic radiosity-based scattering model for vegetation was developed and used to compute vegetation indices for various configurations. The leaf reflectance and transmittance was modeled using the PROSPECT model for various amounts of water, chlorophyll and variable leaf structure. The soil background was modeled using SOILSPEC with a linear mixture of reflectances of sand, clay and peat. A neural network and a geometry based retrieval scheme were used to retrieve leaf area index and chlorophyll concentration for dense canopies. Only simulated canopy reflectances in the 6 visible through short wave IR Landsat TM channels were used. The authors used an empirical function to compute the signal-to-noise ratio of a retrieved quantity.
Tail estimates for stochastic fixed point equations via nonlinear renewal theory
DEFF Research Database (Denmark)
Collamore, Jeffrey F.; Vidyashankar, Anand N.
2013-01-01
estimate P(V>u)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward...... iteration of the given stochastic fixed point equation. In the process, we establish several new results in the realm of nonlinear renewal theory for these processes. As a consequence of our techniques, we also establish a new characterization of the extremal index. Finally, we provide some extensions...... of our methods to Markov-driven processes....
Theory for stationary nonlinear wave propagation in complex magnetic geometry
International Nuclear Information System (INIS)
Watanabe, T.; Hojo, H.; Nishikawa, Kyoji.
1977-08-01
We present our recent efforts to derive a systematic calculation scheme for nonlinear wave propagation in the self-consistent plasma profile in complex magnetic-field geometry. Basic assumptions and/or approximations are i) use of the collisionless two-fluid model with an equation of state; ii) restriction to a steady state propagation and iii) existence of modified magnetic surface, modification due to Coriolis' force. We discuss four situations: i) weak-field propagation without static flow, ii) arbitrary field strength with flow in axisymmetric system, iii) weak field limit of case ii) and iv) arbitrary field strength in nonaxisymmetric torus. Except for case iii), we derive a simple variation principle, similar to that of Seligar and Whitham, by introducing appropriate coordinates. In cases i) and iii), we derive explicit results for quasilinear profile modification. (auth.)
Geometrical theory of nonlinear phase distortion of intense laser beams
International Nuclear Information System (INIS)
Glaze, J.A.; Hunt, J.T.; Speck, D.R.
1975-01-01
Phase distortion arising from whole beam self-focusing of intense laser pulses with arbitrary spatial profiles is treated in the limit of geometrical optics. The constant shape approximation is used to obtain the phase and angular distribution of the geometrical rays in the near field. Conditions for the validity of this approximation are discussed. Geometrical focusing of the aberrated beam is treated for the special case of a beam with axial symmetry. Equations are derived that show both the shift of the focus and the distortion of the intensity distribution that are caused by the nonlinear index of refraction of the optical medium. An illustrative example treats the case of beam distortion in a Nd:Glass amplifier
Linear and nonlinear theory study of Alpha Virginis
International Nuclear Information System (INIS)
Cox, A.N.; Hodson, S.W.; Clancy, S.P.
1981-01-01
Nonlinear radiation hydrodynamic calculations using a model for α Virginis, a β Cephei star, have been made to see if the cause of the recurrent radial pulsation epochs can be discovered. The basic observed characteristics of β Cephei variables are presented. A review of the various proposals to make these stars pulsate concludes that the excitation mechanism must be in the central convective core or variable composition regions. The envelope damps radial fundamental mode pulsations in 4 years and in even shorter periods for radial overtones. It is proposed here that the mixing of envelope hydrogen into the hydrogen depleted (or even exhausted) core can produce periodic pressure pulses which drive the pulsation amplitude up to the observed value. During the decay of the pulsations, evolution toward higher luminosities enables further episodes of mixing and driving to occur. We predict rapid amplitude increases when mixing occurs and a slow decay of radial (and nonradial modes for other β Cephei variables) between mixing episodes
International Nuclear Information System (INIS)
Wang, Lin; Liu, Xiongwei; Renevier, Nathalie; Stables, Matthew; Hall, George M.
2014-01-01
Due to the increasing size and flexibility of large wind turbine blades, accurate and reliable aeroelastic modelling is playing an important role for the design of large wind turbines. Most existing aeroelastic models are linear models based on assumption of small blade deflections. This assumption is not valid anymore for very flexible blade design because such blades often experience large deflections. In this paper, a novel nonlinear aeroelastic model for large wind turbine blades has been developed by combining BEM (blade element momentum) theory and mixed-form formulation of GEBT (geometrically exact beam theory). The nonlinear aeroelastic model takes account of large blade deflections and thus greatly improves the accuracy of aeroelastic analysis of wind turbine blades. The nonlinear aeroelastic model is implemented in COMSOL Multiphysics and validated with a series of benchmark calculation tests. The results show that good agreement is achieved when compared with experimental data, and its capability of handling large deflections is demonstrated. Finally the nonlinear aeroelastic model is applied to aeroelastic modelling of the parked WindPACT 1.5 MW baseline wind turbine, and reduced flapwise deflection from the nonlinear aeroelastic model is observed compared to the linear aeroelastic code FAST (Fatigue, Aerodynamics, Structures, and Turbulence). - Highlights: • A novel nonlinear aeroelastic model for wind turbine blades is developed. • The model takes account of large blade deflections and geometric nonlinearities. • The model is reliable and efficient for aeroelastic modelling of wind turbine blades. • The accuracy of the model is verified by a series of benchmark calculation tests. • The model provides more realistic aeroelastic modelling than FAST (Fatigue, Aerodynamics, Structures, and Turbulence)
International Nuclear Information System (INIS)
Luyt, P.C.B.; Theron, N.J.; Pietra, F.
2017-01-01
It is well known that gasket creep-relaxation results in a reduction of contact pressure between the surface of a gasket and the face of a flange over an extended period of time. This reduction may result in the subsequent failure of the circular bolted flange connection due to leakage. In this paper a pair of flat and raised face integral flanges, PN 10 DN 50 (in accordance with the European EN 1092-1 standard), with non-asbestos compressed fibre ring gaskets with aramid and a nitrile rubber binder were considered. Finite element modelling and analyses were done, for both the circular bolted flange configurations, during the seating condition. The results of the finite element analyses were experimentally validated. It was found that the number of bolt tightening increments as well as the time between the bolt tightening increments had a significant impact on the effect which gasket creep-relaxation had after the seating condition. An increase in either the number of bolting increments or the time between the bolting increments will reduce the effect which gasket creep-relaxation has once the bolts had been fastened. Based on these results it is possible to develop an optimisation scheme to minimize the effect which gasket creep-relaxation has on the contact pressure between the face of the flange and the gasket, after seating, by either increasing or decreasing the number of bolt tightening increments or the time between the bolt tightening increments. - Highlights: • Number of bolt tightening increments and time between bolt tightening increments had significant impact on effect of gasket creep-relaxation after the seating condition. • Impact of gasket creep-relaxation during seating and operating phases investigated by means of finite element analysis and experimentally verified. • Possible to develop optimisation scheme to minimize effect ofh gasket creep-relaxation on contact pressure between flange face and gasket. • Knowing the contact pressure is
Revision of Drucker-Prager cap creep modelling of pebble beds in fusion blankets
International Nuclear Information System (INIS)
Hofer, D.; Kamlah, M.; Hermsmeyer, S.
2004-01-01
A continuum model commonly used in soil mechanics analysis is compiled by use of a finite element software and has been used to simulate the thermomechanical behaviour of pebble beds. The Drucker-Prager Cap theory accounts for inelastic volume change, cap hardening, nonlinear elasticity and pressure dependent shear failure. The hardening mechanism allows for defining the hydrostatic pressure yield stress as a function of the volumetric inelastic strain. Volumetric creep is considered in order to simulate the pebble bed behaviour at high temperatures. Here, the strain hardening option has been used for the consolidation creep mechanism. The model has been calibrated using the fitting curves of the oedometric test given by Reimann et al. The fitted data has been used to calculate a pebble bed with simplified boundary conditions loaded by non-uniform volumetric heating. This calculation demonstrated that the model is capable of representing creep behaviour under volumetric heating conditions. (author)
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
1992-12-01
Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to eliminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science
Analysis of irradiation creep and the structural integrity of fusion in-vessel components
International Nuclear Information System (INIS)
Karditsas, Panayiotis J.
2000-01-01
This paper presents a brief review of the irradiation creep mechanism, analyses of the effect on the performance and behaviour of fusion in-vessel components, and discusses procedures for the estimation of in-service time (or lifetime) of components under combined creep-fatigue. The irradiation creep models and proposed theories are examined and analysed to produce a creep law relevant to fusion conditions. The necessary material data, constitutive equations and other parameters needed for estimation of in-service time from the combination of creep and fatigue damage are identified. Wherever possible, design curves are proposed for stress and strain. Time dependent non-linear elastoplastic example calculations are performed, for a typical first wall structure under power plant loading conditions, assuming austenitic and martensitic steel as structural materials, including material irradiation creep. The results of calculations for the stress and strain history of the first wall are used together with the proposed cumulative damage expressions derived in this study to estimate the in-service time, including the effects of stress relaxation due to creep, reduction of ductility (or fracture strain) and helium-to-displacement-damage ratio. The calculations give a displacement damage of ∼70 dpa for the 316 austenitic steel and ∼110-130 dpa for the martensitic steel. Provided there are no power transients, for a design strain of 0.5%, the in-service time is estimated to be ∼3 years for the 316 steel case (at 2.2 MW/m 2 wall load) and the high wall loading martensitic steel (5.0 MW/m 2 case), and ∼5.3 years for the martensitic steel at lower wall load (2.2 MW/m 2 case). The difficulty in defending these results lies in the uncertainty arising from the limited database and experience of the material properties, especially the creep constitutive law, when exposed to fusion environments
Advanced nonlinear theory: Long-term stability at the SSC
International Nuclear Information System (INIS)
Heifets, S.
1987-01-01
This paper discussed the long-term stability of the particle beams in the Superconducting Super Collider. In particular the dynamics of a single particle beam is considered in depth. The topics of this paper include: the Hamiltonian of this particle approach, perturbation theory, canonical transformations, interaction of the resonances, structure of the phase space, synchro-Betatron oscillations, modulation diffusion and noise-resonance interaction. 36 refs
Stochastic Control Theory, Nonlinear Structural Mechanics and Applied Combinatorics
1989-05-12
More specifically: (") x 3 PAS and Steiner triple systems; (") x 4 PAS and Steiner triple systems which can be nested; and (’) x 5 PAS and Steiner ...am Rudolf Wille CONCEPTUAL SCALING Technische Hochschule Darmstadt Abstract: Scaling of empirical data uses formal patterns to lead to a better...of Arizona Jan 18 - 22 Wille, Rudolf Technische Hochschule Darmstadt Jan 17 - 23 21 APPLICATIONS OF COMBINATORICS AND GRAPH THEORY TO THE BIOLOGICAL
Kinetic theory of nonlinear transport phenomena in complex plasmas
International Nuclear Information System (INIS)
Mishra, S. K.; Sodha, M. S.
2013-01-01
In contrast to the prevalent use of the phenomenological theory of transport phenomena, a number of transport properties of complex plasmas have been evaluated by using appropriate expressions, available from the kinetic theory, which are based on Boltzmann's transfer equation; in particular, the energy dependence of the electron collision frequency has been taken into account. Following the recent trend, the number and energy balance of all the constituents of the complex plasma and the charge balance on the particles is accounted for; the Ohmic loss has also been included in the energy balance of the electrons. The charging kinetics for the complex plasma comprising of uniformly dispersed dust particles, characterized by (i) uniform size and (ii) the Mathis, Rumpl, and Nordsieck power law of size distribution has been developed. Using appropriate expressions for the transport parameters based on the kinetic theory, the system of equations has been solved to investigate the parametric dependence of the complex plasma transport properties on the applied electric field and other plasma parameters; the results are graphically illustrated.
Nucleon-nucleon scattering in the functional quantum theory of the nonlinear spinor field
International Nuclear Information System (INIS)
Haegele, G.
1979-01-01
The author calculates the S matrix for the elastic nucleon-nucleon scattering in the lowest approximation using the quantum theory of nonlinear spinor fields with special emphasis to the ghost configuration of this theory. Introducing a general scalar product a new functional channel calculus is considered. From the results the R and T matrix elements and the differential and integral cross sections are derived. (HSI)
Imaging theory of nonlinear second harmonic and third harmonic generations in confocal microscopy
Institute of Scientific and Technical Information of China (English)
TANG Zhilie; XING Da; LIU Songhao
2004-01-01
The imaging theory of nonlinear second harmonic generation (SHG) and third harmonic generation (THG) in confocal microscopy is presented in this paper. The nonlinear effect of SHG and THG on the imaging properties of confocal microscopy has been analyzed in detail by the imaging theory. It is proved that the imaging process of SHG and THG in confocal microscopy, which is different from conventional coherent imaging or incoherent imaging, can be divided into two different processes of coherent imaging. The three-dimensional point spread functions (3D-PSF) of SHG and THG confocal microscopy are derived based on the nonlinear principles of SHG and THG. The imaging properties of SHG and THG confocal microscopy are discussed in detail according to its 3D-PSF. It is shown that the resolution of SHG and THG confocal microscopy is higher than that of single-and two-photon confocal microscopy.
Nonlinear many-body reaction theories from nuclear mean field approximations
International Nuclear Information System (INIS)
Griffin, J.J.
1983-01-01
Several methods of utilizing nonlinear mean field propagation in time to describe nuclear reaction have been studied. The property of physical asymptoticity is analyzed in this paper, which guarantees that the prediction by a reaction theory for the physical measurement of internal fragment properties shall not depend upon the precise location of the measuring apparatus. The physical asymptoticity is guaranteed in the Schroedinger collision theory of a scuttering system with translationally invariant interaction by the constancy of the S-matrix elements and by the translational invariance of the internal motion for well-separated fragments. Both conditions are necessary for the physical asymptoticity. The channel asymptotic single-determinantal propagation can be described by the Dirac-TDHF (time dependent Hartree-Fock) time evolution. A new asymptotic Hartree-Fock stationary phase (AHFSP) description together with the S-matrix time-dependent Hartree-Fock (TD-S-HF) theory constitute the second example of a physically asymptotic nonlinear many-body reaction theory. A review of nonlinear mean field many-body reaction theories shows that initial value TDHF is non-asymptotic. The TD-S-HF theory is asymptotic by the construction. The gauge invariant periodic quantized solution of the exact Schroedinger problem has been considered to test whether it includes all of the exact eigenfunctions as it ought to. It did, but included as well an infinity of all spurions solutions. (Kato, T.)
Using system theory and energy methods to prove existence of non-linear PDE's
Zwart, H.J.
2015-01-01
In this discussion paper we present an idea of combining techniques known from systems theory with energy estimates to show existence for a class of non-linear partial differential equations (PDE's). At the end of the paper a list of research questions with possible approaches is given.
Stochastic Finite Element Analysis of Non-Linear Structures Modelled by Plasticity Theory
DEFF Research Database (Denmark)
Frier, Christian; Sørensen, John Dalsgaard
2003-01-01
A Finite Element Reliability Method (FERM) is introduced to perform reliability analyses on two-dimensional structures in plane stress, modeled by non-linear plasticity theory. FERM is a coupling between the First Order Reliability Method (FORM) and the Finite Element Method (FEM). FERM can be us...
Chaos Theory as a Model for Life Transitions Counseling: Nonlinear Dynamics and Life's Changes
Bussolari, Cori J.; Goodell, Judith A.
2009-01-01
Chaos theory is presented for counselors working with clients experiencing life transitions. It is proposed as a model that considers disorder, unpredictability, and lack of control as normal parts of transition processes. Nonlinear constructs from physics are adapted for use in counseling. The model provides a method clients can use to…
Non-linear wave loads and ship responses by a time-domain strip theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
. Based on this time-domain strip theory, an efficient non-linear hydroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented as a Timoshenko beam. Numerical calculations are presented for the S175 Containership...
Banks, H. T.; Kunisch, K.
1982-01-01
Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.
White noise theory of robust nonlinear filtering with correlated state and observation noises
Bagchi, Arunabha; Karandikar, Rajeeva
1992-01-01
In the direct white noise theory of nonlinear filtering, the state process is still modeled as a Markov process satisfying an Ito stochastic differential equation, while a finitely additive white noise is used to model the observation noise. In the present work, this asymmetry is removed by modeling
White noise theory of robust nonlinear filtering with correlated state and observation noises
Bagchi, Arunabha; Karandikar, Rajeeva
1994-01-01
In the existing `direct¿ white noise theory of nonlinear filtering, the state process is still modelled as a Markov process satisfying an Itô stochastic differential equation, while a `finitely additive¿ white noise is used to model the observation noise. We remove this asymmetry by modelling the
A Study of the Creep Effect in Loudspeaker Suspension
DEFF Research Database (Denmark)
Agerkvist, Finn T.; Thorborg, Knud; Tinggaard, Carsten
2008-01-01
This paper investigates the creep effect, the visco elastic behaviour of loudspeaker suspension parts, which can be observed as an increase in displacement far below the resonance frequency. The creep effect means that the suspension cannot be modelled as a simple spring. The need for an accurate...... creep model is even larger as the validity of loudspeaker models are now sought extended far into the nonlinear domain of the loudspeaker. Different creep models are investigated and implemented both in simple lumped parameter models as well as time domain non-linear models, the simulation results...
Non-linear electrodynamics in Kaluza-Klein theory
International Nuclear Information System (INIS)
Kerner, R.
1987-01-01
The most general variational principle based on the invariants of the Riemann tensor and leading to the second order differential equations should contain, in dimensions higher than four, the invariants of the Gauss-Bonnet type. In five dimensions the lagrangian should be a linear combination of the scalar curvature and the second-order invariant. The equations of the electromagnetic field are derived in the absence of scalar and gravitational fields of the Kaluza-Klein model. They yield the unique extension of Maxwell's system in the Kaluza-Klein theory. Some properties of eventual solutions are discussed [fr
Classical and Quantum Nonlinear Integrable Systems: Theory and Application
International Nuclear Information System (INIS)
Brzezinski, Tomasz
2003-01-01
This is a very interesting collection of introductory and review articles on the theory and applications of classical and quantum integrable systems. The book reviews several integrable systems such as the KdV equation, vertex models, RSOS and IRF models, spin chains, integrable differential equations, discrete systems, Ising, Potts and other lattice models and reaction--diffusion processes, as well as outlining major methods of solving integrable systems. These include Lax pairs, Baecklund and Miura transformations, the inverse scattering method, various types of the Bethe Ansatz, Painleve methods, the dbar method and fusion methods to mention just a few. The book is divided into two parts, each containing five chapters. The first part is devoted to classical integrable systems and introduces the subject through the KdV equation, and then proceeds through Painleve analysis, discrete systems and two-dimensional integrable partial differential equations, to culminate in the review of solvable lattice models in statistical physics, solved through the coordinate and algebraic Bethe Ansatz methods. The second part deals with quantum integrable systems, and begins with an outline of unifying approaches to quantum, statistical, ultralocal and non-ultralocal systems. The theory and methods of solving quantum integrable spin chains are then described. Recent developments in applying Bethe Ansatz methods in condensed matter physics, including superconductivity and nanoscale physics, are reviewed. The book concludes with an introduction to diffusion-reaction processes. Every chapter is devoted to a different subject and is self-contained, and thus can be read separately. A reader interesting in classical methods of solitons, such as the methods of solving the KdV equation, can start from Chapter 1, while a reader interested in the Bethe Ansatz method can immediately proceed to Chapter 5, and so on. Thus the book should appeal and be useful to a wide range of theoretical
Theory of plasmonic effects in nonlinear optics: the case of graphene
Rostami, Habib; Katsnelson, Mikhail I.; Polini, Marco; Mikhail I. Katsnelson Collaboration; Habib Rostami; Marco Polini Collaboration
The nonlinear optical properties of two-dimensional electronic systems are beginning to attract considerable interest both in the theoretical and experimental sectors. Recent experiments on the nonlinear optical properties of graphene reveal considerably strong third harmonic generation and four-wave mixing of this single-atomic-layer electronic system. We develop a large-N theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved. This work was supported by Fondazione Istituto Italiano di Tecnologia, the European Union's Horizon 2020 research and innovation programme under Grant agreement No. 696656 GrapheneCore, and the ERC Advanced Grant 338957 FEMTO/NANO (M.I.K.).
Relativistic mean-field theory for unstable nuclei with non-linear σ and ω terms
International Nuclear Information System (INIS)
Sugahara, Y.; Toki, H.
1994-01-01
We search for a new parameter set for the description of stable as well as unstable nuclei in the wide mass range within the relativistic mean-field theory. We include a non-linear ω self-coupling term in addition to the non-linear σ self-coupling terms, the necessity of which is suggested by the relativistic Brueckner-Hartree-Fock (RBHF) theory of nuclear matter. We find two parameter sets, one of which is for nuclei above Z=20 and the other for nuclei below that. The calculated results agree very well with the existing data for finite nuclei. The parameter set for the heavy nuclei provides the equation of state of nuclear matter similar to the one of the RBHF theory. ((orig.))
Deformation by grain boundary sliding and slip creep versus diffusional creep
International Nuclear Information System (INIS)
Ruano, O A; Sherby, O D; Wadsworth, J.
1998-01-01
A review is presented of the debates between the present authors and other investigators regarding the possible role of diffusional creep in the plastic flow of polycrystalline metals at low stresses. These debates are recorded in eleven papers over the past seventeen years. ln these papers it has been shown that the creep rates of materials in the so-called diffusional creep region are almost always higher than those predicted by the diffusional creep theory. Additionally, the predictions of grain size effects and stress exponents from diffusional creep theory are often not found in the experimental data. Finally, denuded zones have been universally considered to be direct evidence for diffusional creep; but, those reported in the literature are shown to be found only under conditions where a high stress exponent is observed. Also, the locations of the denuded zones do not match those predicted. Alternative mechanisms are described in which diffusion-controlled dislocation creep and/or grain boundary sliding are the dominant deformation processes in low-stress creep. It is proposed that denuded zones are formed by stress-directed grain boundary migration with the precipitates dissolving in the moving grain boundaries. The above observations have led us to the conclusion that grain boundary sliding and slip creep are in fact the principal mechanisms for observations of plastic flow in the so-called diffusional creep regions
Kharin, Nikolay A.
2000-04-01
In nonlinear ultrasound imaging the images are formed using the second harmonic energy generated due to the nonlinear nature of finite amplitude propagation. This propagation can be modeled using the KZK wave equation. This paper presents further development of nonlinear diffractive field theory based on the KZK equation and its solution by means of the slowly changing profile method for moderate nonlinearity. The analytical expression for amplitudes and phases of sum frequency wave are obtained in addition to the second harmonic wave. Also, the analytical expression for the relative curvature of the wave fronts of fundamental and second harmonic signals are derived. The media with different nonlinear properties and absorption coefficients were investigated to characterize the diffractive field of the transducer at medical frequencies. All expressions demonstrate good agreement with experimental results. The expressions are novel and provide an easy way for prediction of amplitude and phase structure of nonlinearly distorted field of a transducer. The sum frequency signal technique could be implemented as well as second harmonic technique to improve the quality of biomedical images. The results obtained are of importance for medical diagnostic ultrasound equipment design.
Concrete creep at transient temperature: constitutive law and mechanism
International Nuclear Information System (INIS)
Chern, J.C.; Bazant, Z.P.; Marchertas, A.H.
1985-01-01
A constitutive law which describes the transient thermal creep of concrete is presented. Moisture and temperature are two major parameters in this constitutive law. Aside from load, creep, cracking, and thermal (shrinkage) strains, stress-induced hygrothermal strains are also included in the analysis. The theory agrees with most types of test data which include basic creep, thermal expansion, shrinkage, swelling, creep at cyclic heating or drying, and creep at heating under compression or bending. Examples are given to demonstrate agreement between the theory and the experimental data. 15 refs., 6 figs
Creep analysis of silicone for podiatry applications.
Janeiro-Arocas, Julia; Tarrío-Saavedra, Javier; López-Beceiro, Jorge; Naya, Salvador; López-Canosa, Adrián; Heredia-García, Nicolás; Artiaga, Ramón
2016-10-01
This work shows an effective methodology to characterize the creep-recovery behavior of silicones before their application in podiatry. The aim is to characterize, model and compare the creep-recovery properties of different types of silicone used in podiatry orthotics. Creep-recovery phenomena of silicones used in podiatry orthotics is characterized by dynamic mechanical analysis (DMA). Silicones provided by Herbitas are compared by observing their viscoelastic properties by Functional Data Analysis (FDA) and nonlinear regression. The relationship between strain and time is modeled by fixed and mixed effects nonlinear regression to compare easily and intuitively podiatry silicones. Functional ANOVA and Kohlrausch-Willians-Watts (KWW) model with fixed and mixed effects allows us to compare different silicones observing the values of fitting parameters and their physical meaning. The differences between silicones are related to the variations of breadth of creep-recovery time distribution and instantaneous deformation-permanent strain. Nevertheless, the mean creep-relaxation time is the same for all the studied silicones. Silicones used in palliative orthoses have higher instantaneous deformation-permanent strain and narrower creep-recovery distribution. The proposed methodology based on DMA, FDA and nonlinear regression is an useful tool to characterize and choose the proper silicone for each podiatry application according to their viscoelastic properties. Copyright © 2016 Elsevier Ltd. All rights reserved.
Scott, Robert C.; Perry, Boyd, III; Pototzky, Anthony S.
1991-01-01
This paper describes and illustrates two matched-filter-theory based schemes for obtaining maximized and time-correlated gust-loads for a nonlinear airplane. The first scheme is computationally fast because it uses a simple one-dimensional search procedure to obtain its answers. The second scheme is computationally slow because it uses a more complex multidimensional search procedure to obtain its answers, but it consistently provides slightly higher maximum loads than the first scheme. Both schemes are illustrated with numerical examples involving a nonlinear control system.
Avetissian, H K; Ghazaryan, A G; Matevosyan, H H; Mkrtchian, G F
2015-10-01
The microscopic quantum theory of plasma nonlinear interaction with the coherent shortwave electromagnetic radiation of arbitrary intensity is developed. The Liouville-von Neumann equation for the density matrix is solved analytically considering a wave field exactly and a scattering potential of plasma ions as a perturbation. With the help of this solution we calculate the nonlinear inverse-bremsstrahlung absorption rate for a grand canonical ensemble of electrons. The latter is studied in Maxwellian, as well as in degenerate quantum plasma for x-ray lasers at superhigh intensities and it is shown that one can achieve the efficient absorption coefficient in these cases.
Haritos, George K.; Ochoa, O. O.
Various papers on creep-fatigue interaction at high temperature are presented. Individual topics addressed include: analysis of elevated temperature fatigue crack growth mechanisms in Alloy 718, physically based microcrack propagation laws for creep-fatigue-environment interaction, in situ SEM observation of short fatigue crack growth in Waspaloy at 700 C under cyclic and dwell conditions, evolution of creep-fatigue life prediction models, TMF design considerations in turbine airfoils of advanced turbine engines. Also discussed are: high temperature fatigue life prediction computer code based on the total strain version of strainrange partitioning, atomic theory of thermodynamics of internal variables, geometrically nonlinear analysis of interlaminar stresses in unsymmetrically laminated plates subjected to uniform thermal loading, experimental investigation of creep crack tip deformation using moire interferometry. (For individual items see A93-31336 to A93-31344)
Comment on the consistency of truncated nonlinear integral equation based theories of freezing
International Nuclear Information System (INIS)
Cerjan, C.; Bagchi, B.; Rice, S.A.
1985-01-01
We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim--Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions
Nonlinear theory for the parametric instability with comparable electron and ion temperatures
International Nuclear Information System (INIS)
Oberman, C.
1972-01-01
The basic linear theory of the parametric instability driven by a pump E 0 sin ω 0 t oscillating near the electron plasma frequency is reviewed. An expression is derived for the temporal nonlinear development of the fluctuation spectrum of the excited waves. For plasma with comparable electron and ion temperatures nonlinear Landau damping of electron plasma waves on ions provides the dominant nonlinearity. The steady state solutions are examined both analytically and numerically in the limit when the spontaneous emission term is small. The characteristics of the plasma wave spectrum agrees well with the general features of ionospheric observations. The enhanced dissipation rate of the pump due to the presence of the fluctuations agrees with laboratory observations. (U.S.)
Theory of nonlinear acoustic forces acting on fluids and particles in microsystems
DEFF Research Database (Denmark)
Karlsen, Jonas Tobias
fundamentally new capabilities in chemical, biomedical, or clinical studies of single cells and bioparticles. This thesis, entitled Theory of nonlinear acoustic forces acting on fluids and particles in microsystems, advances the fundamental understanding of acoustofluidics by addressing the origin...... of the nonlinear acoustic forces acting on fluids and particles. Classical results in nonlinear acoustics for the non-dissipative acoustic radiation force acting on a particle or an interface, as well as the dissipative acoustic force densities driving acoustic streaming, are derived and discussed in terms...... in the continuous fluid parameters of density and compressibility, e.g., due to a solute concentration field, the thesis presents novel analytical results on the acoustic force density acting on inhomogeneous fluids in acoustic fields. This inhomogeneity-induced acoustic force density is non-dissipative in origin...
Quantum theory from a nonlinear perspective Riccati equations in fundamental physics
Schuch, Dieter
2018-01-01
This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in ...
Nonlinear scattering from a plasma column. I - Theory. II Special cases
Crawford, F. W.; Harker, K. J.
1983-01-01
The scattered signal excited by nonlinear mixing of two plane waves normally incident on an infinitely long column of plasma is investigated. A general solution is obtained for the polarization in which the electric field vectors of the waves are perpendicular to the column axis and the column is assumed to be radically inhomogeneous. This general theory is then applied to the special cases of the inhomogeneous column in the long-wavelength limit, and the homogeneous column both for the general case and in the long-wavelength limit. It is determined that dipole and quadrupole components should predominate in the polar radiation pattern for the long-wavelength case. The special case of second harmonic generation due to a single incident wave is analyzed in detail. Nonlinear scattering coefficients are computed, and the corresponding polar radiation patterns are determined. The findings of this study are employed to evaluate the feasibility of observing nonlinear scattering from meteor trails.
Directory of Open Access Journals (Sweden)
C. P. Borstad
2013-12-01
Full Text Available Around the perimeter of Antarctica, much of the ice sheet discharges to the ocean through floating ice shelves. The buttressing provided by ice shelves is critical for modulating the flux of ice into the ocean, and the presently observed thinning of ice shelves is believed to be reducing their buttressing capacity and contributing to the acceleration and thinning of the grounded ice sheet. However, relatively little attention has been paid to the role that fractures play in the ability of ice shelves to sustain and transmit buttressing stresses. Here, we present a new framework for quantifying the role that fractures play in the creep deformation and buttressing capacity of ice shelves. We apply principles of continuum damage mechanics to derive a new analytical relation for the creep of an ice shelf that accounts for the softening influence of fractures on longitudinal deformation using a state damage variable. We use this new analytical relation, combined with a temperature calculation for the ice, to partition an inverse method solution for ice shelf rigidity into independent solutions for softening damage and stabilizing backstress. Using this new approach, field and remote sensing data can be utilized to monitor the structural integrity of ice shelves, their ability to buttress the flow of ice at the grounding line, and thus their indirect contribution to ice sheet mass balance and global sea level. We apply this technique to the Larsen C ice shelf using remote sensing and Operation IceBridge data, finding damage in areas with known crevasses and rifts. Backstress is highest near the grounding line and upstream of ice rises, in agreement with patterns observed on other ice shelves. The ice in contact with the Bawden ice rise is weakened by fractures, and additional damage or thinning in this area could diminish the backstress transmitted upstream. We model the consequences for the ice shelf if it loses contact with this small ice rise
Effect of microstructure on light ion irradiation creep in nickel
International Nuclear Information System (INIS)
Henager, C.H. Jr.; Simonen, E.P.; Bradley, E.R.; Stang, R.G.
1983-01-01
The concept of inhomogeneous slip or localized deformation is introduced to account for a weak dependence of irradiation creep on initial microstructure. Specimens of pure nickel (Ni) with three different microstructures were irradiated at 473 K with 15-17 MeV deuterons in the Pacific Northwest Laboratory (PNL) light ion irradiation creep apparatus. A dispersed barrier model for Climb-Glide (CG) creep was unable to account for the observed creep rates and creep strains. The weak dependence on microstructure was consistent with the Stress Induced Preferential Absorption (SIPA) creep mechanism but a high stress enhanced bias had to be assumed to account for the creep rates. Also, SIPA was unable to account for the observed creep strains. The CG and SIPA modeling utilized rate theory calculations of point defect fluxes and transmission electron microscopy for sink sizes and densities. (orig.)
Effects of microstructure on light ion irradiation creep in nickel
International Nuclear Information System (INIS)
Henager, C.H. Jr.; Simonen, E.P.; Bradley, E.R.; Stang, R.G.
1982-10-01
The concept of inhomogeneous slip or localized deformation is introduced to account for a weak dependence of irradiation creep on initial microstructure. Specimens of pure Ni with three different microstructures were irradiated at 473 0 K with 15 to 17 MeV deuterons in the PNL light ion irradiation creep apparatus. A dispersed barrier model for climb-glide creep was unable to account for the observed creep rates and creep strains. The weak dependence on microstructure was consistent with the SIPA creep mechanism but a high stress enhanced bias had to be assumed to account for the creep rates. Also, SIPA was unable to account for the observed creep strains. The modeling utilized rate theory calculations of point defect fluxes and transmission electron microscopy for sink sizes and densities
Diffusion creep and its inhibition in a stainless steel
International Nuclear Information System (INIS)
Crossland, I.G.; Clay, B.D.
1977-01-01
The creep of 20% Cr, 25% Ni, Nb stainless steel was examined at low stresses and temperatures around 0.55 T/sub m/. The initial creep behaviour was consistent with the Coble theory of grain boundary diffusion creep; however, steady state creep was not observed and the creep rates quickly fell below the Coble theoretical values although they still remained greater than the Herring--Nabarro predictions. This reduction in creep rate was attributable to an increase in the effective viscosity of the steel rather than to any change in threshold stress. A model is proposed which explains the initial creep rates as being due to Coble creep with elastic accommodation at grain boundary particles. At higher strains grain boundary collapse caused by vacancy sinking is accommodated at precipitate particles by plastic deformation of the adjacent matrix material. 11 figures
International Nuclear Information System (INIS)
Qian, Hong
2011-01-01
The nonlinear dynamics of biochemical reactions in a small-sized system on the order of a cell are stochastic. Assuming spatial homogeneity, the populations of n molecular species follow a multi-dimensional birth-and-death process on Z n . We introduce the Delbrück–Gillespie process, a continuous-time Markov jump process, whose Kolmogorov forward equation has been known as the chemical master equation, and whose stochastic trajectories can be computed via the Gillespie algorithm. Using simple models, we illustrate that a system of nonlinear ordinary differential equations on R n emerges in the infinite system size limit. For finite system size, transitions among multiple attractors of the nonlinear dynamical system are rare events with exponentially long transit times. There is a separation of time scales between the deterministic ODEs and the stochastic Markov jumps between attractors. No diffusion process can provide a global representation that is accurate on both short and long time scales for the nonlinear, stochastic population dynamics. On the short time scale and near deterministic stable fixed points, Ornstein–Uhlenbeck Gaussian processes give linear stochastic dynamics that exhibit time-irreversible circular motion for open, driven chemical systems. Extending this individual stochastic behaviour-based nonlinear population theory of molecular species to other biological systems is discussed. (invited article)
Prediction of the creep properties of discontinuous fibre composites from the matrix creep law
International Nuclear Information System (INIS)
Bilde-Soerensen, J.B.; Boecker Pedersen, O.; Lilholt, H.
1975-02-01
Existing theories for predicting the creep properties of discontinuous fibre composites with non-creeping fibres from matrix creep properties, originally based on a power law, are extended to include an exponential law, and in principle a general matrixlaw. An analysis shows that the composite creep curve can be obtained by a simple displacement of the matrix creep curve in a log sigma vs. log epsilon diagram. This principle, that each point on the matrix curve has a corresponding point on the composite curve,is given a physical interpretation. The direction of displacement is such that the transition from a power law toan exponential law occurs at a lower strain rate for the composite than for the unreinforced matrix. This emphasizes the importance of the exponential creep range in the creep of fibre composites. The combined use of matrix and composite data may allow the creep phenomenon to be studied over a larger range of strain rates than otherwise possible. A method for constructing generalized composite creep diagrams is suggested. Creep properties predicted from matrix data by the present analysis are compared with experimental data from the literature. (author)
International Nuclear Information System (INIS)
Budgor, A.B.; West, B.J.
1978-01-01
We employ the equivalence between Zwanzig's projection-operator formalism and perturbation theory to demonstrate that the approximate-solution technique of statistical linearization for nonlinear stochastic differential equations corresponds to the lowest-order β truncation in both the consolidated perturbation expansions and in the ''mass operator'' of a renormalized Green's function equation. Other consolidated equations can be obtained by selectively modifying this mass operator. We particularize the results of this paper to the Duffing anharmonic oscillator equation
On the theory of weak turbulence for the nonlinear Schrödinger equation
Escobedo, M
2015-01-01
The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.
International Nuclear Information System (INIS)
Di Dong; Yiming Long.
1994-10-01
In this paper, the iteration formula of the Maslov-type index theory for linear Hamiltonian systems with continuous periodic and symmetric coefficients is established. This formula yields a new method to determine the minimality of the period for solutions of nonlinear autonomous Hamiltonian systems via their Maslov-type indices. Applications of this formula give new results on the existence of periodic solutions with prescribed minimal period for such systems. (author). 40 refs
Nonlinear analysis of the cooperation of strategic alliances through stochastic catastrophe theory
Xu, Yan; Hu, Bin; Wu, Jiang; Zhang, Jianhua
2014-04-01
The excitation intervention of strategic alliance may change with the changes in the parameters of circumstance (e.g., external alliance tasks). As a result, the stable cooperation between members may suffer a complete unplanned betrayal at last. However, current perspectives on strategic alliances cannot adequately explain this transition mechanism. This study is a first attempt to analyze this nonlinear phenomenon through stochastic catastrophe theory (SCT). A stochastic dynamics model is constructed based on the cooperation of strategic alliance from the perspective of evolutionary game theory. SCT explains the discontinuous changes caused by the changes in environmental parameters. Theoretically, we identify conditions where catastrophe can occur in the cooperation of alliance members.
T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory
Takahashi, Wataru
1995-01-01
The papers collected in this volume are contributions to T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory, which was held at Keio University, July 2-4, 1993. The conference was organized by Tokyo Institute of Technology (T. I. Tech.) and the Keio Economic Society (K. E. S.) , and supported by Nihon Keizai Shimbun Inc .. A lot of economic problems can be formulated as constrained optimiza tions and equilibrations of their solutions. Nonlinear-convex analysis has been supplying economists with indispensable mathematical machineries for these problems arising in economic theory. Conversely, mathematicians working in this discipline of analysis have been stimulated by various mathematical difficulties raised by economic the ories. Although our special emphasis was laid upon "nonlinearity" and "con vexity" in relation with economic theories, we also incorporated stochastic aspects of financial economics in our project taking account of the remark able rapid growth of this dis...
Documentation for the viscoplastic and creep program
DEFF Research Database (Denmark)
Bellini, Anna
2004-01-01
of this workpackage is to simulate creep behavior of aluminum cast samples subjected to high temperature. In this document a two-state variables unified model is applied in order to simulate creep behavior and time-dependent metallurgical changes. The fundamental assumption of the unified theory is that creep...... is run using the material data obtained through the mentioned experimental study. The results obtained for the simulation of tensile tests and of creep tests are compared with experimental curves, showing a good agreement. Moreover, the document describes the results obtained during the first...... is quite stable and convergence can be reached also with big time steps. Keywords: Viscoplasticity, creep, unified constitutive model, aluminum, high temperature....
International Nuclear Information System (INIS)
Eleonskij, V.M.; Kulagin, N.E.; Novozhilova, N.S.; Silin, V.P.
1984-01-01
The reasons which prevent the existence of periodic in time and self-localised in space solutions of the nonlinear wave equation u=F (u) are determined by the methods of qualitative theory of dynamical systems. The correspondence between the qualitative behaviour of special (separatrix) trajectories in the phase space and asymptotic solutions of the nonlinear wave equation is analysed
φq-field theory for portfolio optimization: “fat tails” and nonlinear correlations
Sornette, D.; Simonetti, P.; Andersen, J. V.
2000-08-01
Physics and finance are both fundamentally based on the theory of random walks (and their generalizations to higher dimensions) and on the collective behavior of large numbers of correlated variables. The archetype examplifying this situation in finance is the portfolio optimization problem in which one desires to diversify on a set of possibly dependent assets to optimize the return and minimize the risks. The standard mean-variance solution introduced by Markovitz and its subsequent developments is basically a mean-field Gaussian solution. It has severe limitations for practical applications due to the strongly non-Gaussian structure of distributions and the nonlinear dependence between assets. Here, we present in details a general analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto Gaussian variables whose covariance matrix provides a new measure of dependence between the non-normal returns, generalizing the covariance matrix into a nonlinear covariance matrix. This nonlinear covariance matrix is chiseled to the specific fat tail structure of the underlying marginal distributions, thus ensuring stability and good conditioning. The portfolio distribution is then obtained as the solution of a mapping to a so-called φq field theory in particle physics, of which we offer an extensive treatment using Feynman diagrammatic techniques and large deviation theory, that we illustrate in details for multivariate Weibull distributions. The interaction (non-mean field) structure in this field theory is a direct consequence of the non-Gaussian nature of the distribution of asset price returns. We find that minimizing the portfolio variance (i.e. the relatively “small” risks) may often increase the large risks, as measured by higher normalized cumulants. Extensive
Tsuchida, Satoshi; Kuratsuji, Hiroshi
2018-05-01
A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker-Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.
Energy Technology Data Exchange (ETDEWEB)
Robinson, Brandon [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering; Rocha da Costa, Leandro Jose [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering; Poirel, Dominique [Royal Military College of Canada, Kingston (Canada). Dept. of Mechanical and Aerospace Engineering; Pettit, Chris [US Naval Academy, Annapolis, MD (United States). Dept. of Mechanical and Aerospace Engineering; Khalil, Mohammad [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Sarkar, Abhijit [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering
2017-09-01
Our study details the derivation of the nonlinear equations of motion for the axial, biaxial bending and torsional vibrations of an aeroelastic cantilever undergoing rigid body (pitch) rotation at the base. The primary attenstion is focussed on the geometric nonlinearities of the system, whereby the aeroelastic load is modeled by the theory of linear quasisteady aerodynamics. This modelling effort is intended to mimic the wind-tunnel experimental setup at the Royal Military College of Canada. While the derivation closely follows the work of Hodges and Dowell [1] for rotor blades, this aeroelastic system contains new inertial terms which stem from the fundamentally different kinematics than those exhibited by helicopter or wind turbine blades. Using the Hamilton’s principle, a set of coupled nonlinear partial differential equations (PDEs) and an ordinary differential equation (ODE) are derived which describes the coupled axial-bending-bending-torsion-pitch motion of the aeroelastic cantilever with the pitch rotation. The finite dimensional approximation of the coupled system of PDEs are obtained using the Galerkin projection, leading to a coupled system of ODEs. Subsequently, these nonlinear ODEs are solved numerically using the built-in MATLAB implicit ODE solver and the associated numerical results are compared with those obtained using Houbolt’s method. It is demonstrated that the system undergoes coalescence flutter, leading to a limit cycle oscillation (LCO) due to coupling between the rigid body pitching mode and teh flexible mode arising from the flapwise bending motion.
Energy Technology Data Exchange (ETDEWEB)
Sadeghi, A., E-mail: a_sadeghi@srbiau.ac.ir [Islamic Azad Univ., Dept. of Mechanical and Aerospace Engineering, Science and Research Branch, Tehran (Iran, Islamic Republic of); Zohoor, H. [Sharif Univ. of Technology, Center of Excellence in Design, Robotics and Automation, Tehran (Iran, Islamic Republic of); The Academy of Sciences if I.R. Iran (Iran, Islamic Republic of)
2010-05-15
The nonlinear flexural vibration for a rectangular atomic force microscope cantilever is investigated by using Timoshenko beam theory. In this paper, the normal and tangential tip-sample interaction forces are found from a Hertzian contact model and the effects of the contact position, normal and lateral contact stiffness, tip height, thickness of the beam, and the angle between the cantilever and the sample surface on the nonlinear frequency to linear frequency ratio are studied. The differential quadrature method is employed to solve the nonlinear differential equations of motion. The results show that softening behavior is seen for most cases and by increasing the normal contact stiffness, the frequency ratio increases for the first mode, but for the second mode, the situation is reversed. The nonlinear-frequency to linear-frequency ratio increases by increasing the Timoshenko beam parameter, but decreases by increasing the contact position for constant amplitude for the first and second modes. For the first mode, the frequency ratio decreases by increasing both of the lateral contact stiffness and the tip height, but increases by increasing the angle α between the cantilever and sample surface. (author)
de Paor, A. M.
Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ɛ has the value 1 is proved via the Popov theorem from feedback system stability theory.
Application of H∞ control theory to power control of a nonlinear reactor model
International Nuclear Information System (INIS)
Suzuki, Katsuo; Shimazaki, Junya; Shinohara, Yoshikuni
1993-01-01
The H∞ control theory is applied to the compensator design of a nonlinear nuclear reactor model, and the results are compared with standard linear quadratic Gaussian (LQG) control. The reactor model is assumed to be provided with a control rod drive system having the compensation of rod position feedback. The nonlinearity of the reactor model exerts a great influence on the stability of the control system, and hence, it is desirable for a power control system of a nuclear reactor to achieve robust stability and to improve the sensitivity of the feedback control system. A computer simulation based on a power control system synthesized by LQG control was performed revealing that the control system has some stationary offset and less stability. Therefore, here, attention is given to the development of a methodology for robust control that can withstand exogenous disturbances and nonlinearity in view of system parameter changes. The developed methodology adopts H∞ control theory in the feedback system and shows interesting features of robustness. The results of the computer simulation indicate that the feedback control system constructed by the developed H∞ compensator possesses sufficient robustness of control on the stability and disturbance attenuation, which are essential for the safe operation of a nuclear reactor
Linear and nonlinear instability theory of a noble gas MHD generator
International Nuclear Information System (INIS)
Mesland, A.J.
1982-01-01
This thesis deals with the stability of the working medium of a seeded noble gas magnetohydrodynamic generator. The aim of the study is to determine the instability mechanism which is most likely to occur in experimental MHD generators and to describe its behaviour with linear and nonlinear theories. In chapter I a general introduction is given. The pertinent macroscopic basic equations are derived in chapter II, viz. the continuity, the momentum and the energy equation for the electrons and the heavy gas particles, consisting of the seed particles and the noble gas atoms. Chapter III deals with the linear plane wave analysis of small disturbances of a homogeneous steady state. The steady state is discussed in chapter IV. The values for the steady state parameters used for the calculations both for the linear analysis as for the nonlinear analysis are made plausible with the experimental values. Based on the results of the linear plane wave theory a nonlinear plane wave model of the electrothermal instability is introduced in chapter V. (Auth.)
A universal nonlinear relation among boundary states in closed string field theory
International Nuclear Information System (INIS)
Kishimoto, Isao; Matsuo, Yutaka; Watanabe, Eitoku
2004-01-01
We show that the boundary states satisfy a nonlinear relation (the idempotency equation) with respect to the star product of closed string field theory. This relation is universal in the sense that various D-branes, including the infinitesimally deformed ones, satisfy the same equation, including the coefficient. This paper generalizes our analysis [hep-th/0306189] in the following senses. (1) We present a background-independent formulation based on conformal field theory. It illuminates the geometric nature of the relation and allows us to more systematically analyze the variations around the D-brane background. (2) We show that the Witten-type star product satisfies a similar relation but with a more divergent coefficient. (3) We determine the coefficient of the relation analytically. The result shows that the α parameter can be formally factored out, and the relation becomes universal. We present a conjecture on vacuum theory based on this computation. (author)
Simultaneous consolidation and creep
DEFF Research Database (Denmark)
Krogsbøll, Anette
1997-01-01
Materials that exhibit creep under constant effective stress typically also show rate dependent behavior. The creep deformations and the rate sensitive behavior is very important when engineering and geological problems with large time scales are considered. When stress induced compaction...
International Nuclear Information System (INIS)
Poirier, J.-P.
1988-01-01
Creep mechanisms for metals, ceramics and rocks, effect of pressure and temperature on deformation processes are considered. The role of crystal defects is analysed, different models of creep are described. Deformation mechanisms maps for different materials are presented
Non-linear gauge transformations in D=10 SYM theory and the BCJ duality
Energy Technology Data Exchange (ETDEWEB)
Lee, Seungjin [Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut,14476 Potsdam (Germany); Mafra, Carlos R. [Institute for Advanced Study, School of Natural Sciences,Einstein Drive, Princeton, NJ 08540 (United States); DAMTP, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Schlotterer, Oliver [Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut,14476 Potsdam (Germany)
2016-03-14
Recent progress on scattering amplitudes in super Yang-Mills and superstring theory benefitted from the use of multiparticle superfields. They universally capture tree-level subdiagrams, and their generating series solve the non-linear equations of ten-dimensional super Yang-Mills. We provide simplified recursions for multiparticle superfields and relate them to earlier representations through non-linear gauge transformations of their generating series. Moreover, we discuss the gauge transformations which enforce their Lie symmetries as suggested by the Bern-Carrasco-Johansson duality between color and kinematics. Another gauge transformation due to Harnad and Shnider is shown to streamline the theta-expansion of multiparticle superfields, bypassing the need to use their recursion relations beyond the lowest components. The findings of this work tremendously simplify the component extraction from kinematic factors in pure spinor superspace.
Influence of magnetic flutter on tearing growth in linear and nonlinear theory
Kreifels, L.; Hornsby, W. A.; Weikl, A.; Peeters, A. G.
2018-06-01
Recent simulations of tearing modes in turbulent regimes show an unexpected enhancement in the growth rate. In this paper the effect is investigated analytically. The enhancement is linked to the influence of turbulent magnetic flutter, which is modelled by diffusion terms in magnetohydrodynamics (MHD) momentum balance and Ohm’s law. Expressions for the linear growth rate as well as the island width in nonlinear theory for small amplitudes are derived. The results indicate an enhanced linear growth rate and a larger linear layer width compared with resistive MHD. Also the island width in the nonlinear regime grows faster in the diffusive model. These observations correspond well to simulations in which the effect of turbulence on the magnetic island width and tearing mode growth is analyzed.
One-dimensional nonlinear theory for rectangular helix traveling-wave tube
Energy Technology Data Exchange (ETDEWEB)
Fu, Chengfang, E-mail: fchffchf@126.com; Zhao, Bo; Yang, Yudong; Ju, Yongfeng [Faculty of Electronic Information Engineering, Huaiyin Institute of Technology, Huai' an 223003 (China); Wei, Yanyu [School of Physical Electronics, University of Electronic and Technology of China, Chengdu 610054 (China)
2016-08-15
A 1-D nonlinear theory of a rectangular helix traveling-wave tube (TWT) interacting with a ribbon beam is presented in this paper. The RF field is modeled by a transmission line equivalent circuit, the ribbon beam is divided into a sequence of thin rectangular electron discs with the same cross section as the beam, and the charges are assumed to be uniformly distributed over these discs. Then a method of computing the space-charge field by solving Green's Function in the Cartesian Coordinate-system is fully described. Nonlinear partial differential equations for field amplitudes and Lorentz force equations for particles are solved numerically using the fourth-order Runge-Kutta technique. The tube's gain, output power, and efficiency of the above TWT are computed. The results show that increasing the cross section of the ribbon beam will improve a rectangular helix TWT's efficiency and reduce the saturated length.
International Nuclear Information System (INIS)
Hahm, T.S.
1990-12-01
Ion temperature gradient turbulence based transport models have difficulties reconciling the recent DIII-D H-mode results where the density profile is flat, but χ e > χ i in the core region. In this work, a nonlinear theory is developed for recently discovered ion temperature gradient trapped electron modes propagating in the electron diamagnetic direction. This instability is predicted to be linearly unstable for L Ti /R approx-lt κ θ ρ s approx-lt (L Ti /R) 1/4 . They are also found to be strongly dispersive even at these long wavelengths, thereby suggesting the importance of the wave-particle-wave interactions in the nonlinear saturation phase. The fluctuation spectrum and anomalous fluxes are calculated. In accordance with the trends observed in DIII-D, the predicted electron thermal diffusivity can be larger than the ion thermal diffusivity. 17 refs., 3 figs
Nonlinear analysis of 0-3 polarized PLZT microplate based on the new modified couple stress theory
Wang, Liming; Zheng, Shijie
2018-02-01
In this study, based on the new modified couple stress theory, the size- dependent model for nonlinear bending analysis of a pure 0-3 polarized PLZT plate is developed for the first time. The equilibrium equations are derived from a variational formulation based on the potential energy principle and the new modified couple stress theory. The Galerkin method is adopted to derive the nonlinear algebraic equations from governing differential equations. And then the nonlinear algebraic equations are solved by using Newton-Raphson method. After simplification, the new model includes only a material length scale parameter. In addition, numerical examples are carried out to study the effect of material length scale parameter on the nonlinear bending of a simply supported pure 0-3 polarized PLZT plate subjected to light illumination and uniform distributed load. The results indicate the new model is able to capture the size effect and geometric nonlinearity.
Creep of granulated loose-fill insulation
DEFF Research Database (Denmark)
Rasmussen, Torben Valdbjørn
This report presents a proposal for a standardised method for creep tests and the necessary theoretical framework that can be used to describe creep of a granulated loose-fill material. Furthermore results from a round robin test are shown. The round robin test was carried out in collaboration...... with SP-Building Physics in Sweden and VTT Building Technology in Finland. For the round robin test a cellulosic fibre insulation material was used. The proposed standardised method for creep tests and theories are limited to cases when the granulated loose-fill material is exposed to a constant...
Tewatia, D K; Tolakanahalli, R P; Paliwal, B R; Tomé, W A
2011-04-07
The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay 'τ' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.
Energy Technology Data Exchange (ETDEWEB)
Tewatia, D K; Tolakanahalli, R P; Paliwal, B R; Tome, W A, E-mail: tewatia@wisc.edu [Department of Human Oncology, University of Wisconsin, Madison, WI (United States)
2011-04-07
The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay '{tau}' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed
International Nuclear Information System (INIS)
Tewatia, D K; Tolakanahalli, R P; Paliwal, B R; Tome, W A
2011-01-01
The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay 'τ' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.
Reassembling Surveillance Creep
DEFF Research Database (Denmark)
Bøge, Ask Risom; Lauritsen, Peter
2017-01-01
We live in societies in which surveillance technologies are constantly introduced, are transformed, and spread to new practices for new purposes. How and why does this happen? In other words, why does surveillance “creep”? This question has received little attention either in theoretical developm......We live in societies in which surveillance technologies are constantly introduced, are transformed, and spread to new practices for new purposes. How and why does this happen? In other words, why does surveillance “creep”? This question has received little attention either in theoretical...... development or in empirical analyses. Accordingly, this article contributes to this special issue on the usefulness of Actor-Network Theory (ANT) by suggesting that ANT can advance our understanding of ‘surveillance creep’. Based on ANT’s model of translation and a historical study of the Danish DNA database......, we argue that surveillance creep involves reassembling the relations in surveillance networks between heterogeneous actors such as the watchers, the watched, laws, and technologies. Second, surveillance creeps only when these heterogeneous actors are adequately interested and aligned. However...
A self-consistent nonlinear theory of resistive-wall instability in a relativistic electron beam
International Nuclear Information System (INIS)
Uhm, H.S.
1994-01-01
A self-consistent nonlinear theory of resistive-wall instability is developed for a relativistic electron beam propagating through a grounded cylindrical resistive tube. The theory is based on the assumption that the frequency of the resistive-wall instability is lower than the cutoff frequency of the waveguide. The theory is concentrated on study of the beam current modulation directly related to the resistive-wall klystron, in which a relativistic electron beam is modulated at the first cavity and propagates downstream through the resistive wall. Because of the self-excitation of the space charge waves by the resistive-wall instability, a highly nonlinear current modulation of the electron beam is accomplished as the beam propagates downstream. A partial integrodifferential equation is obtained in terms of the initial energy modulation (ε), the self-field effects (h), and the resistive-wall effects (κ). Analytically investigating the partial integrodifferential equation, a scaling law of the propagation distance z m at which the maximum current modulation occurs is obtained. It is found in general that the self-field effects dominate over the resistive-wall effects at the beginning of the propagation. As the beam propagates farther downstream, the resistive-wall effects dominate. Because of a relatively large growth rate of the instability, the required tube length of the klystron is short for most applications
timber joists subjected to creep-rupture
African Journals Online (AJOL)
user
Developed non-linear regression models for prediction of safety ... In (3), A, B, C and D are model parameters. ... material parameters. q is given as a function of creep exponent ... Table 1: Stochastic models of the basic design variables. S/No.
A normal form approach to the theory of nonlinear betatronic motion
International Nuclear Information System (INIS)
Bazzani, A.; Todesco, E.; Turchetti, G.; Servizi, G.
1994-01-01
The betatronic motion of a particle in a circular accelerator is analysed using the transfer map description of the magnetic lattice. In the linear case the transfer matrix approach is shown to be equivalent to the Courant-Snyder theory: In the normal coordinates' representation the transfer matrix is a pure rotation. When the nonlinear effects due to the multipolar components of the magnetic field are taken into account, a similar procedure is used: a nonlinear change of coordinates provides a normal form representation of the map, which exhibits explicit symmetry properties depending on the absence or presence of resonance relations among the linear tunes. The use of normal forms is illustrated in the simplest but significant model of a cell with a sextupolar nonlinearity which is described by the quadratic Henon map. After recalling the basic theoretical results in Hamiltonian dynamics, we show how the normal forms describe the different topological structures of phase space such as KAM tori, chains of islands and chaotic regions; a critical comparison with the usual perturbation theory for Hamilton equations is given. The normal form theory is applied to compute the tune shift and deformation of the orbits for the lattices of the SPS and LHC accelerators, and scaling laws are obtained. Finally, the correction procedure of the multipolar errors of the LHC, based on the analytic minimization of the tune shift computed via the normal forms, is described and the results for a model of the LHC are presented. This application, relevant for the lattice design, focuses on the advantages of normal forms with respect to tracking when parametric dependences have to be explored. (orig.)
Creep in commercially pure metals
International Nuclear Information System (INIS)
Nabarro, F.R.N.
2006-01-01
The creep of commercially pure polycrystalline metals under constant stress has four stages: a virtually instantaneous extension, decelerating Andrade β creep, almost steady-state Andrade κ creep, and an acceleration towards failure. Little is known about the first stage, and the fourth stage has been extensively reviewed elsewhere. The limited experimental evidence on the physical mechanism of the second stage is reviewed and a critical discussion is given of various theories of this stage. The dependence of strain rate on stress in the third, steady-state, period seems to fall into two regimes, a power law with an exponent of about 4-5, and a rather closely exponential law. The limits of the parameters within which a simple theory of the exponential dependence can be expected to be valid are discussed, and found to be compatible with experiments. Theories of the power-law dependence are discussed, and, appear to be unconvincing. The theoretical models do not relate closely to the metallographic and other physical observations. In view of the weakness of theory, experiments which may indicate the physical processes dominant in steady-state creep are reviewed. It is usually not clear whether they pertain to the power-law or the exponential regime. While the theories all assume that most of the deformation occurs homogeneously within the grains, most experimental observations point strongly to a large deformation at or close to the grain boundaries. However, a detailed study of dislocation processes in a single grain of polycrystalline foil strained in the electron microscope shows that most of the observed strain can be accounted for by the motion of single dislocations through the subgrain structure. There is no clear reconciliation of these two sets of observations. Grain-boundary sliding cannot occur without intragranular deformation. One or other process may dominate the overall deformation; the geometrically dominant process may not be the rate
Numerically and experimentally analysis of creep
International Nuclear Information System (INIS)
Fontanive, J.A.
1982-11-01
The problems of creep in concrete are analyzed experimentally and numerically, comparing with classical methods and suggesting a numerical procedure for the solution of these problems. Firstly, fundamentals of viscoelasticity and its application to concrete behaviour representation are presented. Then the theories of Dischinger and Arutyunyan are studied, and a computing numerical solutions are compared in several examples. Finally, experiences on creep and relaxation are described, and its result are analyzed. Some coments on possible future developments are included. (Author) [pt
On the treatment of nonlinear local feedbacks within advanced nodal generalized perturbation theory
International Nuclear Information System (INIS)
Maldonado, G.I.; Turinsky, P.J.; Kropaczek, D.J.
1993-01-01
Recent efforts to upgrade the underlying neutronics formulations within the in-core nuclear fuel management optimization code FORMOSA (Ref. 1) have produced two important developments; first, a computationally efficient and second-order-accurate advanced nodal generalized perturbation theory (GPT) model [derived from the nonlinear iterative nodal expansion method (NEM)] for evaluating core attributes (i.e., k eff and power distribution versus cycle burnup), and second, an equally efficient and accurate treatment of local thermal-hydraulic and fission product feedbacks embedded within NEM GPT. The latter development is the focus of this paper
Simplified non-linear time-history analysis based on the Theory of Plasticity
DEFF Research Database (Denmark)
Costa, Joao Domingues
2005-01-01
This paper aims at giving a contribution to the problem of developing simplified non-linear time-history (NLTH) analysis of structures which dynamical response is mainly governed by plastic deformations, able to provide designers with sufficiently accurate results. The method to be presented...... is based on the Theory of Plasticity. Firstly, the formulation and the computational procedure to perform time-history analysis of a rigid-plastic single degree of freedom (SDOF) system are presented. The necessary conditions for the method to incorporate pinching as well as strength degradation...
Nonlinear field theories and non-Gaussian fluctuations for near-critical many-body systems
International Nuclear Information System (INIS)
Tuszynski, J.A.; Dixon, J.M.; Grundland, A.M.
1994-01-01
This review article outlines a number of efforts made over the past several decades to understand the physics of near critical many-body systems. Beginning with the phenomenological theories of Landau and Ginzburg the paper discusses the two main routes adopted in the past. The first approach is based on statistical calculations while the second investigates the underlying nonlinear field equations. In the last part of the paper we outline a generalisation of these methods which combines classical and quantum properties of the many-body systems studied. (orig.)
Naturalness of Nonlinear Scalar Self-Couplings in a Relativistic Mean Field Theory for Neutron Stars
International Nuclear Information System (INIS)
Maekawa, Claudio; Razeira, Moises; Vasconcellos, Cesar A. Z.; Dillig, Manfred; Bodmann, Bardo E. J.
2004-01-01
We investigate the role of naturalness in effective field theory. We focus on dense hadronic matter using a generalized relativistic multi-baryon lagrangian density mean field approach which contains nonlinear self-couplings of the σ, δ meson fields and the fundamental baryon octet. We adjust the model parameters to describe bulk static properties of ordinary nuclear matter. Then, we show that our approach represents a natural modelling of nuclear matter under the extreme conditions of density as the ones found in the interior of neutron stars
Extensions to a nonlinear finite-element axisymmetric shell model based on Reissner's shell theory
International Nuclear Information System (INIS)
Cook, W.A.
1981-01-01
Extensions to shell analysis not usually associated with shell theory are described in this paper. These extensions involve thick shells, nonlinear materials, a linear normal stress approximation, and a changing shell thickness. A finite element shell-of-revolution model has been developed to analyze nuclear material shipping containers under severe impact conditions. To establish the limits for this shell model, the basic assumptions used in its development were studied; these are listed in this paper. Several extensions were evident from the study of these limits: a thick shell, a plastic hinge, and a linear normal stress
Current and Future Constraints on Higgs Couplings in the Nonlinear Effective Theory
Energy Technology Data Exchange (ETDEWEB)
de Blas, Jorge [INFN, Padua; Eberhardt, Otto [Valencia U., IFIC; Krause, Claudius [Fermilab
2018-03-02
We perform a Bayesian statistical analysis of the constraints on the nonlinear Effective Theory given by the Higgs electroweak chiral Lagrangian. We obtain bounds on the effective coefficients entering in Higgs observables at the leading order, using all available Higgs-boson signal strengths from the LHC runs 1 and 2. Using a prior dependence study of the solutions, we discuss the results within the context of natural-sized Wilson coefficients. We further study the expected sensitivities to the different Wilson coefficients at various possible future colliders. Finally, we interpret our results in terms of some minimal composite Higgs models.
Generalized effective potential in nonlinear theories of the 4-th order
International Nuclear Information System (INIS)
Ananikyan, N.S.; Savvidy, G.K.
1980-01-01
By means of the Legendre transformations in the framework of nonlinear theories of the 4-th order a generalized effective potential GITA(phi, G, H, S) is constructed. It depends on PHI, a possible expectation value of the quantum field; on G, H, possible expectation values of the 2- a.nd 3-point connected Green functions and on S= a possible expectation value of the classical action. The expansion for the functional GITA(phi, G, H, S) is obtained, which is similar to the loop expansion for the effective action GITA(phi)
Pelleg, Joshua
2017-01-01
This textbook is one of its kind, since there are no other books on Creep in Ceramics. The book consist of two parts: A and B. In part A general knowledge of creep in ceramics is considered, while part B specifies creep in technologically important ceramics. Part B covers creep in oxide ceramics, carnides and nitrides. While covering all relevant information regarding raw materials and characterization of creep in ceramics, the book also summarizes most recent innovations and developments in this field as a result of extensive literature search.
Zhang, X. F.; Hu, S. D.; Tzou, H. S.
2014-12-01
Converting vibration energy to useful electric energy has attracted much attention in recent years. Based on the electromechanical coupling of piezoelectricity, distributed piezoelectric zero-curvature type (e.g., beams and plates) energy harvesters have been proposed and evaluated. The objective of this study is to develop a generic linear and nonlinear piezoelectric shell energy harvesting theory based on a double-curvature shell. The generic piezoelectric shell energy harvester consists of an elastic double-curvature shell and piezoelectric patches laminated on its surface(s). With a current model in the closed-circuit condition, output voltages and energies across a resistive load are evaluated when the shell is subjected to harmonic excitations. Steady-state voltage and power outputs across the resistive load are calculated at resonance for each shell mode. The piezoelectric shell energy harvesting mechanism can be simplified to shell (e.g., cylindrical, conical, spherical, paraboloidal, etc.) and non-shell (beam, plate, ring, arch, etc.) distributed harvesters using two Lamé parameters and two curvature radii of the selected harvester geometry. To demonstrate the utility and simplification procedures, the generic linear/nonlinear shell energy harvester mechanism is simplified to three specific structures, i.e., a cantilever beam case, a circular ring case and a conical shell case. Results show the versatility of the generic linear/nonlinear shell energy harvesting mechanism and the validity of the simplification procedures.
International Nuclear Information System (INIS)
Maldonado, G.I.; Turinsky, P.J.
1995-01-01
The determination of the family of optimum core loading patterns for pressurized water reactors (PWRs) involves the assessment of the core attributes for thousands of candidate loading patterns. For this reason, the computational capability to efficiently and accurately evaluate a reactor core's eigenvalue and power distribution versus burnup using a nodal diffusion generalized perturbation theory (GPT) model is developed. The GPT model is derived from the forward nonlinear iterative nodal expansion method (NEM) to explicitly enable the preservation of the finite difference matrix structure. This key feature considerably simplifies the mathematical formulation of NEM GPT and results in reduced memory storage and CPU time requirements versus the traditional response-matrix approach to NEM. In addition, a treatment within NEM GPT can account for localized nonlinear feedbacks, such as that due to fission product buildup and thermal-hydraulic effects. When compared with a standard nonlinear iterative NEM forward flux solve with feedbacks, the NEM GPT model can execute between 8 and 12 times faster. These developments are implemented within the PWR in-core nuclear fuel management optimization code FORMOSA-P, combining the robustness of its adaptive simulated annealing stochastic optimization algorithm with an NEM GPT neutronics model that efficiently and accurately evaluates core attributes associated with objective functions and constraints of candidate loading patterns
Game Theory of Tumor–Stroma Interactions in Multiple Myeloma: Effect of Nonlinear Benefits
Directory of Open Access Journals (Sweden)
Javad Salimi Sartakhti
2018-05-01
Full Text Available Cancer cells and stromal cells often exchange growth factors with paracrine effects that promote cell growth: a form of cooperation that can be studied by evolutionary game theory. Previous models have assumed that interactions between cells are pairwise or that the benefit of a growth factor is a linear function of its concentration. Diffusible factors, however, affect multiple cells and generally have nonlinear effects, and these differences are known to have important consequences for evolutionary dynamics. Here, we study tumor–stroma paracrine signaling using a model with multiplayer collective interactions in which growth factors have nonlinear effects. We use multiple myeloma as an example, modelling interactions between malignant plasma cells, osteoblasts, and osteoclasts. Nonlinear benefits can lead to results not observed in linear models, including internal mixed stable equilibria and cyclical dynamics. Models with linear effects, therefore, do not lead to a meaningful characterization of the dynamics of tumor–stroma interactions. To understand the dynamics and the effect of therapies it is necessary to estimate the shape of the benefit functions experimentally and parametrize models based on these functions.
Glimpses of soliton theory the algebra and geometry of nonlinear PDEs
Kasman, Alex
2010-01-01
Solitons are explicit solutions to nonlinear partial differential equations exhibiting particle-like behavior. This is quite surprising, both mathematically and physically. Waves with these properties were once believed to be impossible by leading mathematical physicists, yet they are now not only accepted as a theoretical possibility but are regularly observed in nature and form the basis of modern fiber-optic communication networks. Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. Assuming only multivariable calculus and linear algebra as prerequisites, this book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstr...
Apparently noninvariant terms of nonlinear sigma models in lattice perturbation theory
International Nuclear Information System (INIS)
Harada, Koji; Hattori, Nozomu; Kubo, Hirofumi; Yamamoto, Yuki
2009-01-01
Apparently noninvariant terms (ANTs) that appear in loop diagrams for nonlinear sigma models are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to 'pion' fields, we employ lattice regularization, in which everything (including the Jacobian) is well defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the pion fields at one-loop and the Jacobian does not play an important role in generating ANTs.
A neuroeconomic theory of rational addiction and nonlinear time-perception.
Takahashi, Taiki
2011-01-01
Neuroeconomic conditions for "rational addiction" (Becker & Murphy 1988) have been unknown. This paper derived the conditions for "rational addiction" by utilizing a nonlinear time-perception theory of "hyperbolic" discounting, which is mathematically equivalent to the q-exponential intertemporal choice model based on Tsallis' statistics. It is shown that (i) Arrow-Pratt measure for temporal cognition corresponds to the degree of irrationality (i.e., Prelec's "decreasing impatience" parameter of temporal discounting) and (ii) rationality in addicts is controlled by a nondimensionalization parameter of the logarithmic time-perception function. Furthermore, the present theory illustrates the possibility that addictive drugs increase impulsivity via dopaminergic neuroadaptation without increasing irrationality. Future directions in the application of the model to studies in neuroeconomics are discussed.
Directory of Open Access Journals (Sweden)
Ryo Oizumi
Full Text Available Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity.
Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi
2016-01-01
Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity.
Connection between Einstein equations, nonlinear sigma models, and self-dual Yang-Mills theory
International Nuclear Information System (INIS)
Sanchez, N.; Whiting, B.
1986-01-01
The authors analyze the connection between nonlinear sigma models self-dual Yang-Mills theory, and general relativity (self-dual and non-self-dual, with and without killing vectors), both at the level of the equations and at the level of the different type of solutions (solitons and calorons) of these theories. They give a manifestly gauge invariant formulation of the self-dual gravitational field analogous to that given by Yang for the self-dual Yang-Mills field. This formulation connects in a direct and explicit way the self-dual Yang-Mills and the general relativity equations. They give the ''R gauge'' parametrization of the self-dual gravitational field (which corresponds to modified Yang's-type and Ernst equations) and analyze the correspondence between their different types of solutions. No assumption about the existence of symmetries in the space-time is needed. For the general case (non-self-dual), they show that the Einstein equations contain an O nonlinear sigma model. This connection with the sigma model holds irrespective of the presence of symmetries in the space-time. They found a new class of solutions of Einstein equations depending on holomorphic and antiholomorphic functions and we relate some subclasses of these solutions to solutions of simpler nonlinear field equations that are well known in other branches of physics, like sigma models, SineGordon, and Liouville equations. They include gravitational plane wave solutions. They analyze the response of different accelerated quantum detector models, compare them to the case when the detectors are linterial in an ordinary Planckian gas at a given temperature, and discuss the anisotropy of the detected response for Rindler observers
Viscoelastic characterization of carbon fiber-epoxy composites by creep and creep rupture tests
International Nuclear Information System (INIS)
Farina, Luis Claudio
2009-01-01
One of the main requirements for the use of fiber-reinforced polymer matrix composites in structural applications is the evaluation of their behavior during service life. The warranties of the integrity of these structural components demand a study of the time dependent behavior of these materials due to viscoelastic response of the polymeric matrix and of the countless possibilities of design configurations. In the present study, creep and creep rupture test in stress were performed in specimens of unidirectional carbon fiber-reinforced epoxy composites with fibers orientations of 60 degree and 90 degree, at temperatures of 25 and 70 degree C. The aim is the viscoelastic characterization of the material through the creep curves to some levels of constant tension during periods of 1000 h, the attainment of the creep rupture envelope by the creep rupture curves and the determination of the transition of the linear for non-linear behavior through isochronous curves. In addition, comparisons of creep compliance curves with a viscoelastic behavior prediction model based on Schapery equation were also performed. For the test, a modification was verified in the behavior of the material, regarding the resistance, stiffness and deformation, demonstrating that these properties were affected for the time and tension level, especially in work temperature above the ambient. The prediction model was capable to represent the creep behavior, however the determination of the equations terms should be considered, besides the variation of these with the applied tension and the elapsed time of test. (author)
A. M. de Paor
1998-01-01
International audience; Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ? has the value 1 is proved via ...
Modelling of creep hysteresis in ferroelectrics
He, Xuan; Wang, Dan; Wang, Linxiang; Melnik, Roderick
2018-05-01
In the current paper, a macroscopic model is proposed to simulate the hysteretic dynamics of ferroelectric ceramics with creep phenomenon incorporated. The creep phenomenon in the hysteretic dynamics is attributed to the rate-dependent characteristic of the polarisation switching processes induced in the materials. A non-convex Helmholtz free energy based on Landau theory is proposed to model the switching dynamics. The governing equation of single-crystal model is formulated by applying the Euler-Lagrange equation. The polycrystalline model is obtained by combining the single crystal dynamics with a density function which is constructed to model the weighted contributions of different grains with different principle axis orientations. In addition, numerical simulations of hysteretic dynamics with creep phenomenon are presented. Comparison of the numerical results and their experimental counterparts is also presented. It is shown that the creep phenomenon is captured precisely, validating the capability of the proposed model in a range of its potential applications.
Testing universal relations of neutron stars with a nonlinear matter-gravity coupling theory
International Nuclear Information System (INIS)
Sham, Y.-H.; Lin, L.-M.; Leung, P. T.
2014-01-01
Due to our ignorance of the equation of state (EOS) beyond nuclear density, there is still no unique theoretical model for neutron stars (NSs). It is therefore surprising that universal EOS-independent relations connecting different physical quantities of NSs can exist. Lau et al. found that the frequency of the f-mode oscillation, the mass, and the moment of inertia are connected by universal relations. More recently, Yagi and Yunes discovered the I-Love-Q universal relations among the mass, the moment of inertia, the Love number, and the quadrupole moment. In this paper, we study these universal relations in the Eddington-inspired Born-Infeld (EiBI) gravity. This theory differs from general relativity (GR) significantly only at high densities due to the nonlinear coupling between matter and gravity. It thus provides us an ideal case to test how robust the universal relations of NSs are with respect to the change of the gravity theory. Due to the apparent EOS formulation of EiBI gravity developed recently by Delsate and Steinhoff, we are able to study the universal relations in EiBI gravity using the same techniques as those in GR. We find that the universal relations in EiBI gravity are essentially the same as those in GR. Our work shows that, within the currently viable coupling constant, there exists at least one modified gravity theory that is indistinguishable from GR in view of the unexpected universal relations.
Testing Universal Relations of Neutron Stars with a Nonlinear Matter-Gravity Coupling Theory
Sham, Y.-H.; Lin, L.-M.; Leung, P. T.
2014-02-01
Due to our ignorance of the equation of state (EOS) beyond nuclear density, there is still no unique theoretical model for neutron stars (NSs). It is therefore surprising that universal EOS-independent relations connecting different physical quantities of NSs can exist. Lau et al. found that the frequency of the f-mode oscillation, the mass, and the moment of inertia are connected by universal relations. More recently, Yagi and Yunes discovered the I-Love-Q universal relations among the mass, the moment of inertia, the Love number, and the quadrupole moment. In this paper, we study these universal relations in the Eddington-inspired Born-Infeld (EiBI) gravity. This theory differs from general relativity (GR) significantly only at high densities due to the nonlinear coupling between matter and gravity. It thus provides us an ideal case to test how robust the universal relations of NSs are with respect to the change of the gravity theory. Due to the apparent EOS formulation of EiBI gravity developed recently by Delsate and Steinhoff, we are able to study the universal relations in EiBI gravity using the same techniques as those in GR. We find that the universal relations in EiBI gravity are essentially the same as those in GR. Our work shows that, within the currently viable coupling constant, there exists at least one modified gravity theory that is indistinguishable from GR in view of the unexpected universal relations.
International Nuclear Information System (INIS)
Kong, Ling-Bao; Wang, Hong-Yu; Hou, Zhi-Ling; Jin, Hai-Bo; Du, Chao-Hai
2013-01-01
The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency. -- Highlights: •The theory of slow-wave electron cyclotron masers is considered. •The calculation of efficiency under the resonance condition is presented. •The efficiency under Gaussian velocity spreads has been obtained
Directory of Open Access Journals (Sweden)
A. M. de Paor
1998-01-01
Full Text Available Hide (Nonlinear Processes in Geophysics, 1998 has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ε has the value 1 is proved via the Popov theorem from feedback system stability theory.
Energy Technology Data Exchange (ETDEWEB)
Kong, Ling-Bao, E-mail: konglingbao@gmail.com [School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 (China); Wang, Hong-Yu [School of Physics, Anshan Normal University, Anshan 114005 (China); Hou, Zhi-Ling, E-mail: houzl@mail.buct.edu.cn [School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 (China); Jin, Hai-Bo [School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081 (China); Du, Chao-Hai [Institute of Electronics, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency. -- Highlights: •The theory of slow-wave electron cyclotron masers is considered. •The calculation of efficiency under the resonance condition is presented. •The efficiency under Gaussian velocity spreads has been obtained.
Interrelation of creep and relaxation: a modeling approach for ligaments.
Lakes, R S; Vanderby, R
1999-12-01
Experimental data (Thornton et al., 1997) show that relaxation proceeds more rapidly (a greater slope on a log-log scale) than creep in ligament, a fact not explained by linear viscoelasticity. An interrelation between creep and relaxation is therefore developed for ligaments based on a single-integral nonlinear superposition model. This interrelation differs from the convolution relation obtained by Laplace transforms for linear materials. We demonstrate via continuum concepts of nonlinear viscoelasticity that such a difference in rate between creep and relaxation phenomenologically occurs when the nonlinearity is of a strain-stiffening type, i.e., the stress-strain curve is concave up as observed in ligament. We also show that it is inconsistent to assume a Fung-type constitutive law (Fung, 1972) for both creep and relaxation. Using the published data of Thornton et al. (1997), the nonlinear interrelation developed herein predicts creep behavior from relaxation data well (R > or = 0.998). Although data are limited and the causal mechanisms associated with viscoelastic tissue behavior are complex, continuum concepts demonstrated here appear capable of interrelating creep and relaxation with fidelity.
Finding a nonlinear lattice with improved integrability using Lie transform perturbation theory
International Nuclear Information System (INIS)
Sonnad, Kiran G.; Cary, John R.
2004-01-01
A condition for improved dynamic aperture for nonlinear, alternating gradient transport systems is derived using Lie transform perturbation theory. The Lie transform perturbation method is used here to perform averaging over fast oscillations by canonically transforming to slowly oscillating variables. This is first demonstrated for a linear sinusoidal focusing system. This method is then employed to average the dynamics over a lattice period for a nonlinear focusing system, provided by the use of higher order poles such as sextupoles and octupoles along with alternate gradient quadrupoles. Unlike the traditional approach, the higher order focusing is not treated as a perturbation. The Lie transform method is particularly advantageous for such a system where the form of the Hamiltonian is complex. This is because the method exploits the property of canonical invariance of Poisson brackets so that the change of variables is accomplished by just replacing the old ones with the new. The analysis shows the existence of a condition in which the system is azimuthally symmetric in the transformed, slowly oscillating frame. Such a symmetry in the time averaged frame renders the system nearly integrable in the laboratory frame. This condition leads to reduced chaos and improved confinement when compared to a system that is not close to integrability. Numerical calculations of single-particle trajectories and phase space projections of the dynamic aperture performed for a lattice with quadrupoles and sextupoles confirm that this is indeed the case
Turning points in nonlinear business cycle theories, financial crisis and the 2007-2008 downturn.
Dore, Mohammed H I; Singh, Ragiv G
2009-10-01
This paper reviews three nonlinear dynamical business cycle theories of which only one (The Goodwin model) reflects the stylized facts of observed business cycles and has a plausible turning point mechanism. The paper then examines the US (and now global) financial crisis of 2008 and the accompanying downturn in the US. The paper argues that a skewed income distribution could not sustain effective demand and that over the 2001-2006 expansion demand was maintained through massive amounts of credit, with more than 50 percent of sales in the US being maintained through credit. A vector autoregression model confirms the crucial role played by credit. However legislative changes that dismantled the restrictions placed on the financial sector after the crash of 1929 and the consequent structural changes in the financial sector after 1980 enabled the growth of new debt instruments and credit. But overexpansion of credit when profits and house prices were declining in 2005/06 led to a nonlinear shift due to a new realization of the poor quality of some of this debt, namely mortgage backed securities. Bankruptcies, followed by retrenchment at the banks, then led to the bursting of the credit bubble, with the possibility of a severe recession.
International Nuclear Information System (INIS)
Qiu Chunrong; Ouyang Zhengbiao; Zhang Shichang; Zhang Huibo; Jin Jianbo; Lai Yingxin
2005-01-01
A self-consistent nonlinear theory for the outer-slotted-coaxial-waveguide cyclotron autoresonance maser (CARM) amplifier is presented, which includes the characteristic equation of the wave, coupling equation of the wave with the relativistic electron beam and the simulation model. The influences of the magnetic field, the slot depth and width are investigated. The interesting characteristic of the device is that the mode competition can be efficiently suppressed by slotting the outer wall of the coaxial waveguide. A typical example is given by the theoretical design of a 137 GHz outer-slotted-coaxial-waveguide CARM amplifier by utilizing an electron beam with a voltage of 90 kV, current of 50 A, velocity pitch angle of 0.85 and a magnetic field of 43.0 kG. The nonlinear simulation predicts a power of 467.9 kW, an electronic efficiency of 10.4% and a saturated gain of 46.7 dB, if the electron beam has no velocity spread. However, the axial velocity spread deteriorates the device; for example, if the axial velocity spread is 2%, the peak power decreases to 332.4 kW with an efficiency of 7.4% and a saturated gain of 45.22 dB. Simulation shows that the efficiency of the outer-slotted-coaxial-waveguide CARM amplifier may be increased from 10.4% to 29.6% by tapering the magnetic field
Nemeth, Michael P.
2014-01-01
Nonlinear and bifurcation buckling equations for elastic, stiffened, geometrically perfect, right-circular cylindrical, anisotropic shells subjected to combined loads are presented that are based on Sanders' shell theory. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated-composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discrepancies between the results obtained by using Donnell's equations and variants of Sanders' equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.
Nonlinear theory of ion-acoustic waves in an ideal plasma with degenerate electrons
International Nuclear Information System (INIS)
Dubinov, A. E.; Dubinova, A. A.
2007-01-01
A nonlinear theory is constructed that describes steady-state ion-acoustic waves in an ideal plasma in which the electron component is a degenerate Fermi gas and the ion component is a classical gas. The parameter ranges in which such a plasma can exist are determined, and dispersion relations for ion-acoustic waves are obtained that make it possible to find the linear ion-acoustic velocity. Analytic gas-dynamic models of ion sound are developed for a plasma with the ion component as a cold, an isothermal, or an adiabatic gas, and moreover, the solutions to the equations of all the models are brought to a quadrature form. Profiles of a subsonic periodic and a supersonic solitary wave are calculated, and the upper critical Mach numbers of a solitary wave are determined. For a plasma with cold ions, the critical Mach number is expressed by an explicit exact formula
[Analysis of the heart sound with arrhythmia based on nonlinear chaos theory].
Ding, Xiaorong; Guo, Xingming; Zhong, Lisha; Xiao, Shouzhong
2012-10-01
In this paper, a new method based on the nonlinear chaos theory was proposed to study the arrhythmia with the combination of the correlation dimension and largest Lyapunov exponent, through computing and analyzing these two parameters of 30 cases normal heart sound and 30 cases with arrhythmia. The results showed that the two parameters of the heart sounds with arrhythmia were higher than those with the normal, and there was significant difference between these two kinds of heart sounds. That is probably due to the irregularity of the arrhythmia which causes the decrease of predictability, and it's more complex than the normal heart sound. Therefore, the correlation dimension and the largest Lyapunov exponent can be used to analyze the arrhythmia and for its feature extraction.
Super long-term creep tests of advanced HP and IP rotor steels
Energy Technology Data Exchange (ETDEWEB)
Tchizhik, A.A. [The Polzunov Central Boiler and Turbine Institute, Department the Fatigue Life of Materials for Power Plans Equipment, St. Petersburg (Russian Federation)
1998-12-31
A creep model has been developed for predicting the long-term creep behavior, in excess of 200,000 h for advanced materials.The new creep theory is based on a continuum microdamage model and is used to calculate the fields of stress and strain and wedge and cavities damage in critical components of steam and gas turbines. The application of this new model increases the reliability and service life of modern turbines. The accuracy of the model to predict long - term creep behavior, creep ductility was verified using the data bank of super long-term creep tests of advanced materials. (orig.) 12 refs.
Super long-term creep tests of advanced HP and IP rotor steels
Energy Technology Data Exchange (ETDEWEB)
Tchizhik, A A [The Polzunov Central Boiler and Turbine Institute, Department the Fatigue Life of Materials for Power Plans Equipment, St. Petersburg (Russian Federation)
1999-12-31
A creep model has been developed for predicting the long-term creep behavior, in excess of 200,000 h for advanced materials.The new creep theory is based on a continuum microdamage model and is used to calculate the fields of stress and strain and wedge and cavities damage in critical components of steam and gas turbines. The application of this new model increases the reliability and service life of modern turbines. The accuracy of the model to predict long - term creep behavior, creep ductility was verified using the data bank of super long-term creep tests of advanced materials. (orig.) 12 refs.
Nondestructive evaluation of creep-fatigue damage: an interim report
International Nuclear Information System (INIS)
Nickell, R.E.
1977-02-01
In view of the uncertainties involved in designing against creep-fatigue failure and the consequences of such failures in Class 1 nuclear components that operate at elevated temperature, the possibility of intermittent or even continuous non-destructive examination of these components has been considered. In this interim report some preliminary results on magnetic force and ultrasonic evaluation of creep-fatigue damage in an LMFBR steam generator material are presented. These results indicate that the non-destructive evaluation of pure creep damage will be extremely difficult. A set of biaxial creep-fatigue tests that are designed to discriminate between various failure theories is also described
Solution of the nonlinear inverse scattering problem by T-matrix completion. I. Theory.
Levinson, Howard W; Markel, Vadim A
2016-10-01
We propose a conceptually different method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology, and other applications. The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. Although we seek a local (diagonally dominated) V as the solution to the posed problem, we allow V to be nonlocal at the intermediate stages of iterations. This allows us to utilize the one-to-one correspondence between V and the T matrix of the problem. Here it is important to realize that not every T corresponds to a diagonal V and we, therefore, relax the usual condition of strict diagonality (locality) of V. An iterative algorithm is proposed in which we seek T that is (i) compatible with the measured scattering data and (ii) corresponds to an interaction potential V that is as diagonally dominated as possible. We refer to this algorithm as to the data-compatible T-matrix completion. This paper is Part I in a two-part series and contains theory only. Numerical examples of image reconstruction in a strongly nonlinear regime are given in Part II [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043318 (2016)10.1103/PhysRevE.94.043318]. The method described in this paper is particularly well suited for very large data sets that become increasingly available with the use of modern measurement techniques and instrumentation.
Brader, J M; Siebenbürger, M; Ballauff, M; Reinheimer, K; Wilhelm, M; Frey, S J; Weysser, F; Fuchs, M
2010-12-01
Using a combination of theory, experiment, and simulation we investigate the nonlinear response of dense colloidal suspensions to large amplitude oscillatory shear flow. The time-dependent stress response is calculated using a recently developed schematic mode-coupling-type theory describing colloidal suspensions under externally applied flow. For finite strain amplitudes the theory generates a nonlinear response, characterized by significant higher harmonic contributions. An important feature of the theory is the prediction of an ideal glass transition at sufficiently strong coupling, which is accompanied by the discontinuous appearance of a dynamic yield stress. For the oscillatory shear flow under consideration we find that the yield stress plays an important role in determining the nonlinearity of the time-dependent stress response. Our theoretical findings are strongly supported by both large amplitude oscillatory experiments (with Fourier transform rheology analysis) on suspensions of thermosensitive core-shell particles dispersed in water and Brownian dynamics simulations performed on a two-dimensional binary hard-disk mixture. In particular, theory predicts nontrivial values of the exponents governing the final decay of the storage and loss moduli as a function of strain amplitude which are in good agreement with both simulation and experiment. A consistent set of parameters in the presented schematic model achieves to jointly describe linear moduli, nonlinear flow curves, and large amplitude oscillatory spectroscopy.
Creep buckling: an experiment, an 'exact' solution and some simple thoughts
International Nuclear Information System (INIS)
Heller, P.; Anderson, R.G.
1986-01-01
The paper presents attempts to analyse and understand a carefully conducted creep buckling experiment. The analysis was conducted using the ABAQUS Finite Element Code coupled to a number of plausible creep laws. The results show good agreement between ABAQUS runs and experimental deflections but it is difficult to reproduce the early loads. A simple model of buckling analysis for n-power creep laws is derived as an aid to understanding the development of the deflections for non-linear creep laws. In particular, the model suggests why deflections develop so rapidly and how the creep deflection development relates to the elastic behaviour. (author)
Nemeth, Michael P.
2013-01-01
A detailed exposition on a refined nonlinear shell theory suitable for nonlinear buckling analyses of laminated-composite shell structures is presented. This shell theory includes the classical nonlinear shell theory attributed to Leonard, Sanders, Koiter, and Budiansky as an explicit proper subset. This approach is used in order to leverage the exisiting experience base and to make the theory attractive to industry. In addition, the formalism of general tensors is avoided in order to expose the details needed to fully understand and use the theory. The shell theory is based on "small" strains and "moderate" rotations, and no shell-thinness approximations are used. As a result, the strain-displacement relations are exact within the presumptions of "small" strains and "moderate" rotations. The effects of transverse-shearing deformations are included in the theory by using analyst-defined functions to describe the through-the-thickness distributions of transverse-shearing strains. Constitutive equations for laminated-composite shells are derived without using any shell-thinness approximations, and simplified forms and special cases are presented.
Experimental verification of creep analyses for prestressed concrete reactor vessels
International Nuclear Information System (INIS)
Aoyagi, Y.; Abe, H.; Ohnuma, H.
1977-01-01
The authors proposed a new method of creep analysis based on the theory of strain hardening, which assumes that accumulated creep at a given time influences the creep after that. This method was applied to calculate step-by-step the behaviors of uniaxial creep of concrete under variable temperatures and stresses, creep in reinforced concrete specimens and the behaviors of prestressed concrete beams under themal gradients. The experimental and calculated results agreed fairly well. Further, this method was incorporated in the finite element creep analysis for the prestressed concrete hollow cylinder and the full scale model. The calculated strain changes with time pursued closely those obtained by experiments. The above led to the conclusion that from the viewpoint of both accuracy and computation time the strain hardening method proposed by the authors may be judged advantageous for practical usages
Creep buckling problems in fast reactor components
International Nuclear Information System (INIS)
Ramesh, R.; Damodaran, S.P.; Chellapandi, P.; Chetal, S.C.; Bhoje, S.B.
1995-01-01
Creep buckling analyses for two important components of 500 M We Prototype Fast Breeder Reactor (PFBR), viz. Intermediate Heat Exchanger (IHX) and Inner Vessel (IV), are reported. The INCA code of CASTEM system is used for the large displacement elasto-plastic-creep analysis of IHX shell. As a first step, INCA is validated for a typical benchmark problem dealing with the creep buckling of a tube under external pressure. Prediction of INCA is also compared with the results obtained using Hoff's theory. For IV, considering the prohibitively high computational cost for the actual analysis, a simplified analysis which involves only large displacement elastoplastic buckling analysis is performed using isochronous stress strain curve approach. From both of these analysis is performed using isochronous stress strain curve approach. From both of these analysis, it has been inferred that creep buckling failure mode is not of great concern in the design of PFBR components. It has also been concluded from the analysis that Creep Cross Over Curve given in RCC-MR is applicable for creep buckling failure mode also. (author). 8 refs., 9 figs., 1 tab
Hindsight Bias Doesn't Always Come Easy: Causal Models, Cognitive Effort, and Creeping Determinism
Nestler, Steffen; Blank, Hartmut; von Collani, Gernot
2008-01-01
Creeping determinism, a form of hindsight bias, refers to people's hindsight perceptions of events as being determined or inevitable. This article proposes, on the basis of a causal-model theory of creeping determinism, that the underlying processes are effortful, and hence creeping determinism should disappear when individuals lack the cognitive…
Directory of Open Access Journals (Sweden)
Iman Eshraghi
2016-09-01
Full Text Available Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.
International Nuclear Information System (INIS)
Pusch, R.; Adey, R.
1999-12-01
The study involved characterization of the microstructural arrangement and molecular forcefields in the buffer clay for getting a basis for selecting suitable creep models. It is concluded that the number of particles and wide range of the particle bond spectrum require that stochastical mechanics and thermodynamics will be considered and they are basic to the creep model proposed for predicting creep settlement of the canisters. The influence of the stress level on creep strain of MX-80 clay is not well known but for the buffer creep is approximately proportional to stress. Theoretical considerations suggest a moderate impact for temperatures up to 90 deg C and this is supported by model experiments. It is believed that the assumption of strain being proportional to temperature is conservative. The general performance of the stochastic model can be illustrated in principle by use of visco-elastic rheological models implying a time-related increase in viscosity. The shear-induced creep settlement under constant volume conditions calculated by using the proposed creep model is on the order of 1 mm in ten thousand years and up to a couple of millimeters in one million years. It is much smaller than the consolidation settlement, which is believed to be on the order of 10 mm. The general conclusion is that creep settlement of the canisters is very small and of no significance to the integrity of the buffer itself or of the canisters
International Nuclear Information System (INIS)
Pelah, I.
1981-03-01
Simulation of fusion-neutron induced damage by beams of light ions is discussed. It is suggested that accelerated creep measurements to determine ''end of life'' of materials may be done by the application of thermal treatment and thermal creep measurements. (author)
Hall, P.; Malik, M. R.
1984-01-01
The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.
Hall, P.; Malik, M. R.
1986-01-01
The instability of a three-dimensional attachment-line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite-amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time-dependent Navier-Stokes equations for the attachment-line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite-amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment-line boundary layer is also investigated.
International Nuclear Information System (INIS)
Mahmoud, Gamal M; Mahmoud, Emad E; Arafa, Ayman A
2013-01-01
In this paper we deal with the projective synchronization (PS) of hyperchaotic complex nonlinear systems and its application in secure communications based on passive theory. The unpredictability of the scaling factor in PS can additionally enhance the security of communications. In this paper, a scheme for secure message transmission is proposed, and we try to transmit more than one large or bounded message from the transmitter to the receiver. The new hyperchaotic complex Lorenz system is employed to encrypt these messages. In the transmitter, the original messages are modulated into its parameter. In the receiver, we assume that the parameter of the receiver system is uncertain. The controllers and corresponding parameter update law are constructed to achieve PS between the transmitter and receiver system with an uncertain parameter, and identify the unknown parameter via passive theory. The original messages can be recovered successfully through some simple operations by the estimated parameter. Numerical results have verified the effectiveness and feasibility of the presented method. (paper)
Theory of coherent Stark nonlinear spectroscopy in a three-level system
International Nuclear Information System (INIS)
Loiko, Yurii; Serrat, Carles
2007-01-01
Coherent Stark nonlinear spectroscopy (CSNS) is a spectroscopic tool based on the cancellation of the phase sensitivity at frequency 5ω in the ultrafast four-wave mixing (FWM) of two-color pulses with frequencies ω and 3ω. We develop a theory for CSNS in three-level V-type systems, and reveal that the mechanism for the phase sensitivity at 5ω is the quantum interference between the two primary paths in the FWM of the ω and 3ω fields. We find that the cancellation phenomenon occurs when the probability amplitude of one of these two primary pathways becomes equal to zero due to the competition effect between the two allowed transitions in the V-type system. The analytical expressions that describe the phase-sensitivity phenomenon and the conditions for its cancellation have been derived on the basis of perturbation theory, and are confirmed by numerical integration of the density matrix and Maxwell equations. We argue that CSNS can be utilized, in particular, for the investigation of optically dense media
Examination of Experimental Data for Irradiation - Creep in Nuclear Graphite
Mobasheran, Amir Sassan
The objective of this dissertation was to establish credibility and confidence levels of the observed behavior of nuclear graphite in neutron irradiation environment. Available experimental data associated with the OC-series irradiation -induced creep experiments performed at the Oak Ridge National Laboratory (ORNL) were examined. Pre- and postirradiation measurement data were studied considering "linear" and "nonlinear" creep models. The nonlinear creep model considers the creep coefficient to vary with neutron fluence due to the densification of graphite with neutron irradiation. Within the range of neutron fluence involved (up to 0.53 times 10^{26} neutrons/m ^2, E > 50 KeV), both models were capable of explaining about 96% and 80% of the variation of the irradiation-induced creep strain with neutron fluence at temperatures of 600^circC and 900^circC, respectively. Temperature and reactor power data were analyzed to determine the best estimates for the actual irradiation temperatures. It was determined according to thermocouple readouts that the best estimate values for the irradiation temperatures were well within +/-10 ^circC of the design temperatures of 600^circC and 900 ^circC. The dependence of the secondary creep coefficients (for both linear and nonlinear models) on irradiation temperature was determined assuming that the variation of creep coefficient with temperature, in the temperature range studied, is reasonably linear. It was concluded that the variability in estimate of the creep coefficients is definitely not the results of temperature fluctuations in the experiment. The coefficients for the constitutive equation describing the overall growth of grade H-451 graphite were also studied. It was revealed that the modulus of elasticity and the shear modulus are not affected by creep and that the electrical resistivity is slightly (less than 5%) changed by creep. However, the coefficient of thermal expansion does change with creep. The consistency of
Creep relaxation of fuel pin bending and ovalling stresses
International Nuclear Information System (INIS)
Chan, D.P.; Jackson, R.J.
1979-06-01
Analytical methods for calculating fuel pin cladding bending and ovalling stresses due to pin bundle-duct mechanical interaction taking into account nonlinear creep are presented. Calculated results are in close agreement with finite element results by MARC-CDC program. The methods are used to investigate the effect of creep on the FTR fuel cladding bending and ovalling stresses. It is concluded that the cladding of 316 SS 20% CW and reference design has high creep rates in the FTR core region to keep the bending and ovalling stresses to low levels
Nonlinear analysis of prestressed concrete reactor pressure vessels
International Nuclear Information System (INIS)
Connor, J.J.
1975-01-01
The numerical procedures for predicting the nonlinear behavior of a prestressed concrete reactor vessel over its design life are discussed. The numerical models are constructed by combining three-dimensional isoparametric finite elements which simulate the concrete, thin shell elements which simulate steel linear plates, and layers of reinforcement steel, and axial elements for discrete prestressing cables. Nonlinearity under compressive stress, multi-dimensional cracking, shrinkage and stress/temperature induced creep of concrete are considered in addition to the elasti-plastic behavior of the liner and reinforcing steel. Various failure theories for concrete have been proposed recently. Also, there are alternative strategies for solving the discrete system equations over the design life, accounting for test loads, pressure and temperature operational loads, creep unloading and abnormal loads. The proposed methods are reviewed, and a new formulation developed by the authors is described. A number of comparisons with experimental tests results and other numerical schemes are presented. These examples demonstrate the validity of the formulation and also provide valuable information concerning the cost and accuracy of the various solution strategies i.e., total vs. incremental loading and initial vs. tangent stiffness. Finally, the analysis of an actual PCRV is described. Stress contours and cracking patterns in the region of cutouts corresponding to operational pressure and temperature loads are illustrated. The effects of creep, unloading, and creep recovery are then shown. Lastly, a strategy for assessing the performance over its design life is discussed
Spherical Indentation Techniques for Creep Property Evaluation Considering Transient Creep
Energy Technology Data Exchange (ETDEWEB)
Lim, Dongkyu; Kim, Minsoo; Lee, Hyungyil [Sogang Univ., Seoul, (Korea, Republic of); Lee, Jin Haeng [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2013-11-15
Creep through nanoindentations has attracted increasing research attention in recent years. Many studies related to indentation creep tests, however, have simply focused on the characteristics of steady-state creep, and there exist wide discrepancies between the uniaxial test and the indentation test. In this study, we performed a computational simulation of spherical indentations, and we proposed a method for evaluating the creep properties onsidering transient creep. We investigated the material behavior with variation of creep properties and expressed it using regression equations for normalized variables. We finally developed a program to evaluate the creep properties considering transient creep. By using the proposed method, we successfully obtained creep exponents with an average error less than 1.1 and creep coefficients with an average error less than 2.3 from the load-depth curve.
Spherical Indentation Techniques for Creep Property Evaluation Considering Transient Creep
International Nuclear Information System (INIS)
Lim, Dongkyu; Kim, Minsoo; Lee, Hyungyil; Lee, Jin Haeng
2013-01-01
Creep through nanoindentations has attracted increasing research attention in recent years. Many studies related to indentation creep tests, however, have simply focused on the characteristics of steady-state creep, and there exist wide discrepancies between the uniaxial test and the indentation test. In this study, we performed a computational simulation of spherical indentations, and we proposed a method for evaluating the creep properties onsidering transient creep. We investigated the material behavior with variation of creep properties and expressed it using regression equations for normalized variables. We finally developed a program to evaluate the creep properties considering transient creep. By using the proposed method, we successfully obtained creep exponents with an average error less than 1.1 and creep coefficients with an average error less than 2.3 from the load-depth curve
Creep properties of discontinuous fibre composites with partly creeping fibres
International Nuclear Information System (INIS)
Bilde-Soerensen, J.B.; Lilholt, H.
1977-05-01
In a previous report (RISO-M-1810) the creep properties of discontinuous fibre composites with non-creeping fibres were analyzed. In the present report this analysis is extended to include the case of discontinuous composites with partly creeping fibres. It is shown that the creep properties of the composite at a given strain rate, epsilonsub(c), depend on the creep properties of the matrix at a strain rate higher than epsilonsub(c), and on the creep properties of the fibres at epsilonsub(c). The composite creep law is presented in a form which permits a graphical determination of the composite creep curve. This can be constructed on the basis of the matrix and the fibre creep curves by vector operations in a log epsilon vs. log sigma diagram. The matrix contribution to the creep strength can be evaluated by a simple method. (author)
Theory and praxis of map analsys in CHEF part 2: Nonlinear normal form
International Nuclear Information System (INIS)
Michelotti, Leo
2009-01-01
This is the second of three memos describing how normal form map analysis is implemented in CHEF. The first (1) explained the manipulations required to assure that initial, linear transformations preserved Poincare invariants, thereby confirming correct normalization of action-angle coordinates. In this one, the transformation will be extended to nonlinear terms. The third, describing how the algorithms were implemented within the software of CHEF's libraries, most likely will never be written. The first section, Section 2, quickly lays out preliminary concepts and relationships. In Section 3, we shall review the perturbation theory - an iterative sequence of transformations that converts a nonlinear mapping into its normal form - and examine the equation which moves calculations from one step to the next. Following that is a section titled 'Interpretation', which identifies connections between the normalized mappings and idealized, integrable, fictitious Hamiltonian models. A final section contains closing comments, some of which may - but probably will not - preview work to be done later. My reasons for writing this memo and its predecessor have already been expressed. (1) To them can be added this: 'black box code' encourages users to proceed with little or no understanding of what it does or how it operates. So far, CHEF has avoided this trap admirably by failing to attract potential users. However, we reached a watershed last year: even I now have difficulty following the software through its maze of operations. Extensions to CHEF's physics functionalities, software upgrades, and even simple maintenance are becoming more difficult than they should. I hope these memos will mark parts of the maze for easier navigation in the future. Despite appearances to the contrary, I tried to include no (or very little) more than the minimum needed to understand what CHEF's nonlinear analysis modules do.1 As with the first memo, material has been lifted - and modified - from
Theory and praxis of map analsys in CHEF part 2: Nonlinear normal form
Energy Technology Data Exchange (ETDEWEB)
Michelotti, Leo; /FERMILAB
2009-04-01
This is the second of three memos describing how normal form map analysis is implemented in CHEF. The first [1] explained the manipulations required to assure that initial, linear transformations preserved Poincare invariants, thereby confirming correct normalization of action-angle coordinates. In this one, the transformation will be extended to nonlinear terms. The third, describing how the algorithms were implemented within the software of CHEF's libraries, most likely will never be written. The first section, Section 2, quickly lays out preliminary concepts and relationships. In Section 3, we shall review the perturbation theory - an iterative sequence of transformations that converts a nonlinear mapping into its normal form - and examine the equation which moves calculations from one step to the next. Following that is a section titled 'Interpretation', which identifies connections between the normalized mappings and idealized, integrable, fictitious Hamiltonian models. A final section contains closing comments, some of which may - but probably will not - preview work to be done later. My reasons for writing this memo and its predecessor have already been expressed. [1] To them can be added this: 'black box code' encourages users to proceed with little or no understanding of what it does or how it operates. So far, CHEF has avoided this trap admirably by failing to attract potential users. However, we reached a watershed last year: even I now have difficulty following the software through its maze of operations. Extensions to CHEF's physics functionalities, software upgrades, and even simple maintenance are becoming more difficult than they should. I hope these memos will mark parts of the maze for easier navigation in the future. Despite appearances to the contrary, I tried to include no (or very little) more than the minimum needed to understand what CHEF's nonlinear analysis modules do.1 As with the first memo, material
Nanoindentation creep versus bulk compressive creep of dental resin-composites.
El-Safty, S; Silikas, N; Akhtar, R; Watts, D C
2012-11-01
To evaluate nanoindentation as an experimental tool for characterizing the viscoelastic time-dependent creep of resin-composites and to compare the resulting parameters with those obtained by bulk compressive creep. Ten dental resin-composites: five conventional, three bulk-fill and two flowable were investigated using both nanoindentation creep and bulk compressive creep methods. For nano creep, disc specimens (15mm×2mm) were prepared from each material by first injecting the resin-composite paste into metallic molds. Specimens were irradiated from top and bottom surfaces in multiple overlapping points to ensure optimal polymerization using a visible light curing unit with output irradiance of 650mW/cm(2). Specimens then were mounted in 3cm diameter phenolic ring forms and embedded in a self-curing polystyrene resin. Following grinding and polishing, specimens were stored in distilled water at 37°C for 24h. Using an Agilent Technologies XP nanoindenter equipped with a Berkovich diamond tip (100nm radius), the nano creep was measured at a maximum load of 10mN and the creep recovery was determined when each specimen was unloaded to 1mN. For bulk compressive creep, stainless steel split molds (4mm×6mm) were used to prepare cylindrical specimens which were thoroughly irradiated at 650mW/cm(2) from multiple directions and stored in distilled water at 37°C for 24h. Specimens were loaded (20MPa) for 2h and unloaded for 2h. One-way ANOVA, Levene's test for homogeneity of variance and the Bonferroni post hoc test (all at p≤0.05), plus regression plots, were used for statistical analysis. Dependent on the type of resin-composite material and the loading/unloading parameters, nanoindentation creep ranged from 29.58nm to 90.99nm and permanent set ranged from 8.96nm to 30.65nm. Bulk compressive creep ranged from 0.47% to 1.24% and permanent set ranged from 0.09% to 0.38%. There was a significant (p=0.001) strong positive non-linear correlation (r(2)=0.97) between bulk
The Volterra's integral equation theory for accelerator single-freedom nonlinear components
International Nuclear Information System (INIS)
Wang Sheng; Xie Xi
1996-01-01
The Volterra's integral equation equivalent to the dynamic equation of accelerator single-freedom nonlinear components is given, starting from which the transport operator of accelerator single-freedom nonlinear components and its inverse transport operator are obtained. Therefore, another algorithm for the expert system of the beam transport operator of accelerator single-freedom nonlinear components is developed
Directory of Open Access Journals (Sweden)
2007-01-01
Full Text Available Hysteresis is a rate-independent non-linearity that is expressed through thresholds, switches, and branches. Exceedance of a threshold, or the occurrence of a turning point in the input, switches the output onto a particular output branch. Rate-independent branching on a very large set of switches with non-local memory is the central concept in the new definition of hysteresis. Hysteretic loops are a special case. A self-consistent mathematical description of hydrological systems with hysteresis demands a new non-linear systems theory of adequate generality. The goal of this paper is to establish this and to show how this may be done. Two results are presented: a conceptual model for the hysteretic soil-moisture characteristic at the pedon scale and a hysteretic linear reservoir at the catchment scale. Both are based on the Preisach model. A result of particular significance is the demonstration that the independent domain model of the soil moisture characteristic due to Childs, Poulavassilis, Mualem and others, is equivalent to the Preisach hysteresis model of non-linear systems theory, a result reminiscent of the reduction of the theory of the unit hydrograph to linear systems theory in the 1950s. A significant reduction in the number of model parameters is also achieved. The new theory implies a change in modelling paradigm.
Gasinski, Leszek
2005-01-01
Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.
Farantos, Stavros C
2014-01-01
This brief presents numerical methods for describing and calculating invariant phase space structures, as well as solving the classical and quantum equations of motion for polyatomic molecules. Examples covered include simple model systems to realistic cases of molecules spectroscopically studied. Vibrationally excited and reacting molecules are nonlinear dynamical systems, and thus, nonlinear mechanics is the proper theory to elucidate molecular dynamics by investigating invariant structures in phase space. Intramolecular energy transfer, and the breaking and forming of a chemical bond have now found a rigorous explanation by studying phase space structures.
Tutcuoglu, A.; Majidi, C.
2014-12-01
Using principles of damped harmonic oscillation with continuous media, we examine electrostatic energy harvesting with a "soft-matter" array of dielectric elastomer (DE) transducers. The array is composed of infinitely thin and deformable electrodes separated by layers of insulating elastomer. During vibration, it deforms longitudinally, resulting in a change in the capacitance and electrical enthalpy of the charged electrodes. Depending on the phase of electrostatic loading, the DE array can function as either an actuator that amplifies small vibrations or a generator that converts these external excitations into electrical power. Both cases are addressed with a comprehensive theory that accounts for the influence of viscoelasticity, dielectric breakdown, and electromechanical coupling induced by Maxwell stress. In the case of a linearized Kelvin-Voigt model of the dielectric, we obtain a closed-form estimate for the electrical power output and a scaling law for DE generator design. For the complete nonlinear model, we obtain the optimal electrostatic voltage input for maximum electrical power output.
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials
Energy Technology Data Exchange (ETDEWEB)
Matouš, Karel, E-mail: kmatous@nd.edu [Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556 (United States); Geers, Marc G.D.; Kouznetsova, Varvara G. [Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven (Netherlands); Gillman, Andrew [Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556 (United States)
2017-02-01
Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials
International Nuclear Information System (INIS)
Matouš, Karel; Geers, Marc G.D.; Kouznetsova, Varvara G.; Gillman, Andrew
2017-01-01
Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials
Matouš, Karel; Geers, Marc G. D.; Kouznetsova, Varvara G.; Gillman, Andrew
2017-02-01
Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.
A nonlinear theory of relativistic klystrons connected to a coaxial waveguide
International Nuclear Information System (INIS)
Uhm, H.S.; Hendricks, K.J.; Arman, M.J.; Bowers, L.; Hackett, K.E.; Spencer, T.A.; Coleman, P.D.; Lemke, R.W.
1997-01-01
A self-consistent nonlinear theory of current modulation in an electron beam propagating through relativistic klystrons connected to a coaxial waveguide is developed. A theoretical model of the beam-energy increase Δγ near the extraction cavity is also developed, based on the self-potential depression. The potential depression κ can be significantly reduced in the vicinity of the extraction cavity from its value at the injection point. In appropriate system parameters, the kinetic-energy increase can easily be more than 50 keV, thereby eliminating the possibility of virtual cathode in the extraction cavity. Properties of the current modulation in a klystron are also investigated, assuming that a regular cylindrical waveguide is connected to a coaxial waveguide at the propagation distance z=z 1 . Due to proximity of a grounded conductor, the beam close-quote s potential depression κ in the coaxial region is considerably less than that in the regular region. It is shown in the present analysis that amplitude of the current modulation increases drastically as the coaxial inner-conductor approaches the driving cavity. Moreover, the amplitude of the current modulation in the coaxial region changes slowly in comparison with that in the regular region
Generalizing a nonlinear geophysical flood theory to medium-sized river networks
Gupta, Vijay K.; Mantilla, Ricardo; Troutman, Brent M.; Dawdy, David; Krajewski, Witold F.
2010-01-01
The central hypothesis of a nonlinear geophysical flood theory postulates that, given space-time rainfall intensity for a rainfall-runoff event, solutions of coupled mass and momentum conservation differential equations governing runoff generation and transport in a self-similar river network produce spatial scaling, or a power law, relation between peak discharge and drainage area in the limit of large area. The excellent fit of a power law for the destructive flood event of June 2008 in the 32,400-km2 Iowa River basin over four orders of magnitude variation in drainage areas supports the central hypothesis. The challenge of predicting observed scaling exponent and intercept from physical processes is explained. We show scaling in mean annual peak discharges, and briefly discuss that it is physically connected with scaling in multiple rainfall-runoff events. Scaling in peak discharges would hold in a non-stationary climate due to global warming but its slope and intercept would change.
International Nuclear Information System (INIS)
Pack, M. V.; Camacho, R. M.; Howell, J. C.
2006-01-01
We present a theory describing the transients and rise times of the refractive Kerr nonlinearity which is enhanced using electromagnetically induced transparency (EIT). We restrict our analysis to the case of a pulsed signal field with continuous-wave EIT fields, and all fields are well below saturation. These restrictions enable the reduction of an EIT Kerr, four-level, density-matrix equation to a two-level Bloch-vector equation which has a simple and physically intuitive algebraic solution. The physically intuitive picture of a two-level Bloch vector provides insights that are easily generalized to more complex and experimentally realistic models. We consider generalization to the cases of Doppler broadening, many-level EIT systems (we consider the D1 line of 87 Rb), and optically thick media. For the case of optically thick media we find that the rise time of the refractive EIT Kerr effect is proportional to the optical thickness. The rise time of the refractive EIT Kerr effect sets important limitations for potential few-photon applications
Time-dependent density functional theory for nonlinear properties of open-shell systems.
Rinkevicius, Zilvinas; Jha, Prakash Chandra; Oprea, Corneliu I; Vahtras, Olav; Agren, Hans
2007-09-21
This paper presents response theory based on a spin-restricted Kohn-Sham formalism for computation of time-dependent and time-independent nonlinear properties of molecules with a high spin ground state. The developed approach is capable to handle arbitrary perturbations and constitutes an efficient procedure for evaluation of electric, magnetic, and mixed properties. Apart from presenting the derivation of the proposed approach, we show results from illustrating calculations of static and dynamic hyperpolarizabilities of small Si(3n+1)H(6n+3) (n=0,1,2) clusters which mimic Si(111) surfaces with dangling bond defects. The results indicate that the first hyperpolarizability tensor components of Si(3n+1)H(6n+3) have an ordering compatible with the measurements of second harmonic generation in SiO2/Si(111) interfaces and, therefore, support the hypothesis that silicon surface defects with dangling bonds are responsible for this phenomenon. The results exhibit a strong dependence on the quality of basis set and exchange-correlation functional, showing that an appropriate set of diffuse functions is required for reliable predictions of the first hyperpolarizability of open-shell compounds.
National Oceanic and Atmospheric Administration, Department of Commerce — Seismic creep is the constant or periodic movement on a fault as contrasted with the sudden rupture associated with an earthquake. It is a usually slow deformation...
Energy Technology Data Exchange (ETDEWEB)
Ubic, Rick; Butt, Darryl; Windes, William
2014-03-13
An understanding of the underlying mechanisms of irradiation creep in graphite material is required to correctly interpret experimental data, explain micromechanical modeling results, and predict whole-core behavior. This project will focus on experimental microscopic data to demonstrate the mechanism of irradiation creep. High-resolution transmission electron microscopy should be able to image both the dislocations in graphite and the irradiation-induced interstitial clusters that pin those dislocations. The team will first prepare and characterize nanoscale samples of virgin nuclear graphite in a transmission electron microscope. Additional samples will be irradiated to varying degrees at the Advanced Test Reactor (ATR) facility and similarly characterized. Researchers will record microstructures and crystal defects and suggest a mechanism for irradiation creep based on the results. In addition, the purchase of a tensile holder for a transmission electron microscope will allow, for the first time, in situ observation of creep behavior on the microstructure and crystallographic defects.
Biaxial Creep Specimen Fabrication
International Nuclear Information System (INIS)
JL Bump; RF Luther
2006-01-01
This report documents the results of the weld development and abbreviated weld qualification efforts performed by Pacific Northwest National Laboratory (PNNL) for refractory metal and superalloy biaxial creep specimens. Biaxial creep specimens were to be assembled, electron beam welded, laser-seal welded, and pressurized at PNNL for both in-pile (JOYO reactor, O-arai, Japan) and out-of-pile creep testing. The objective of this test campaign was to evaluate the creep behavior of primary cladding and structural alloys under consideration for the Prometheus space reactor. PNNL successfully developed electron beam weld parameters for six of these materials prior to the termination of the Naval Reactors program effort to deliver a space reactor for Project Prometheus. These materials were FS-85, ASTAR-811C, T-111, Alloy 617, Haynes 230, and Nirnonic PE16. Early termination of the NR space program precluded the development of laser welding parameters for post-pressurization seal weldments
Biaxial Creep Specimen Fabrication
Energy Technology Data Exchange (ETDEWEB)
JL Bump; RF Luther
2006-02-09
This report documents the results of the weld development and abbreviated weld qualification efforts performed by Pacific Northwest National Laboratory (PNNL) for refractory metal and superalloy biaxial creep specimens. Biaxial creep specimens were to be assembled, electron beam welded, laser-seal welded, and pressurized at PNNL for both in-pile (JOYO reactor, O-arai, Japan) and out-of-pile creep testing. The objective of this test campaign was to evaluate the creep behavior of primary cladding and structural alloys under consideration for the Prometheus space reactor. PNNL successfully developed electron beam weld parameters for six of these materials prior to the termination of the Naval Reactors program effort to deliver a space reactor for Project Prometheus. These materials were FS-85, ASTAR-811C, T-111, Alloy 617, Haynes 230, and Nirnonic PE16. Early termination of the NR space program precluded the development of laser welding parameters for post-pressurization seal weldments.
International Nuclear Information System (INIS)
Taroco, E.; Feijoo, R.A.
1981-07-01
In this paper it is presented a variational method for the limit analysis of an ideal plastic solid. This method has been denominated as Modified Secundary Creep and enables to find the collapse loads through a minimization of a functional and a limit process. Given an ideal plastic material it is shown how to determinate the associated secundary creep constitutive equation. Finally, as an application, it is found the limit load in an pressurized von Mises rigid plastic sphere. (Author) [pt
On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics
DEFF Research Database (Denmark)
True, Hans
1999-01-01
We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined...... of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed......., and the important case of multiple equilibrium states and their dependence on a parameter is discussed. It is argued that the analysis of nonlinear dynamic problems always should start with an analysis of the equilibrium states of the full nonlinear problem whereby great care must be taken in the choice...
Creep fatigue damage under multiaxial conditions
International Nuclear Information System (INIS)
Lobitz, D.W.; Nickell, R.E.
1977-01-01
When structural components are subjected to severe cyclic loading conditions with intermittent periods of sustained loading at elevated temperature, the designer must guard against a failure mode caused by the interaction of time-dependent and time-independent deformation. This phenomena is referred to as creep-fatigue interaction. The most elementary form of interaction theory (called linear damage summation) is now embodied in the ASME Boiler and Pressure Vessel Code. In recent years, a competitor for the linear damage summation theory has emerged, called strainrange partitioning. This procedure is based upon the visualization of the cyclic strain in a uniaxial creep-fatigue test as a hysteresis loop, with the inelastic strains in the loop counter-balanced in one of two ways. The two theories are compared and contrasted in terms of ease of use, possible inconsistencies, and component life prediction. Future work to further test the damage theories is recommended
Creep fatigue design of FBR components
International Nuclear Information System (INIS)
Bhoje, S.B.; Chellapandi, P.
1997-01-01
This paper deals with the characteristic features of Fast Breeder Reactor (FBR) with reference to creep fatigue, current creep fatigue design approach in compliance with RCCMR (1987) design code, material data, effects of weldments and neutron irradiation, material constitutive models employed, structural analysis and further R and D required for achieving maturity in creep fatigue design of FBR components. For the analysis reported in this paper, material constitutive models developed based on ORNIb (Oak Ridge National Laboratory) and Chaboche viscoplastic theories are employed to demonstrate the potential of FBR components for higher plant temperatures and/or longer life. The results are presented for the studies carried out towards life prediction of Prototype Fast Breeder Reactor (PFBR) components. (author). 24 refs, 8 figs, 5 tabs
Nonlinear theory of surface-wave--particle interactions in a cylindrical plasma
International Nuclear Information System (INIS)
Dengra, A.; Palop, J.I.F.
1994-01-01
This work is an application of the specular reflection hypothesis to the study of the nonlinear surface-wave--particle interactions in a cylindrical plasma. The model is based on nonlinear resolution of the Vlasov equation by the method of characteristics. The expression obtained for the rate of increase of kinetic energy per electron has permitted us to investigate the temporal behavior of nonlinear collisionless damping for different situations as a function of the critical parameters
International Nuclear Information System (INIS)
McDeavitt, S.M.; Solomon, A.A.
1997-01-01
Uranium-10 wt % zirconium (U-10Zr) is a fuel alloy that has been used in the Experimental Breeder Reactor-II (EBR-II). The high burnup that was desired in this fuel system made high demands on the mechanical compatibility between fuel and cladding both during normal operation and during safety-related transients when rapid differential expansion may cause high stresses. In general, this mechanical stress can be reduced by cladding deformation if the cladding is sufficiently ductile at high burnup, and/or by fuel hot-pressing. Fortunately, the fuel is very porous when it contacts the cladding, but this porosity gradually fills with solid fission products (primarily lanthanides) that may limit the fuel's compressibility. If the porosity remains open, gaseous fission products are released and the porous fuel creeps rather than hot-presses under contact stresses. If the pores are closed by sintering or by solid fission products, the porous fuel will hot-isostatic press (HIP), as represented by the models to be discussed. HIP experiments performed at 700 C on U-10Zr samples with different impurity phase contents (Part 1) are analyzed in terms of several creep cavitation models. The coupled diffusion/creep cavitation model of Chen and Argon shows good quantitative agreement with measured HIP rates for hydride- and metal-derived U-10Zr materials, assuming that pores are uniformly distributed on grain boundaries and are of modal size, and that far-field strain rates are negligible. The analysis predicts, for the first time, an asymmetry between HIP and swelling at identical pressure-induced driving forces due to differences in grain boundary stresses. The differences in compressibility of hydride- and metal-derived U-10Zr can be partially explained by differences in pore size and spacing. The relevance of the experiments to description of in-reactor densification under external pressure or contact stress due to fuel/cladding mechanical interaction is discussed
Irradiation creep in zirconium single crystals
International Nuclear Information System (INIS)
MacEwen, S.R.; Fidleris, V.
1976-07-01
Two identical single crystals of crystal bar zirconium have been creep tested in reactor. Both specimens were preirradiated at low stress to a dose of about 4 x 10 23 n/m 2 (E > 1 MeV), and were then loaded to 25 MPa. The first specimen was loaded with reactor at full power, the second during a shutdown. The loading strain for both crystals was more than an order of magnitude smaller than that observed when an identical unirradiated crystal was loaded to the same stress. Both crystals exhibited periods of primary creep, after which their creep rates reached nearly constant values when the reactor was at power. During shutdowns the creep rates decreased rapidly with time. Electron microscopy revealed that the irradiation damage consisted of prismatic dislocation loops, approximately 13.5 nm in diameter. Cleared channels, identified as lying on (1010) planes, were also observed. The results are discussed in terms of the current theories for flux enhanced creep in the light of the microstructures observed. (author)
Energy Technology Data Exchange (ETDEWEB)
Zahariev, Federico; Gordon, Mark S., E-mail: mark@si.msg.chem.iastate.edu [Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States)
2014-05-14
This work presents an extension of the linear response TDDFT/EFP method to the nonlinear-response regime together with the implementation of nonlinear-response TDDFT/EFP in the quantum-chemistry computer package GAMESS. Included in the new method is the ability to calculate the two-photon absorption cross section and to incorporate solvent effects via the EFP method. The nonlinear-response TDDFT/EFP method is able to make correct qualitative predictions for both gas phase values and aqueous solvent shifts of several important nonlinear properties.
Enhanced flux creep and nonequilibrium optical response in YBaCuO epitaxial films
International Nuclear Information System (INIS)
Zeldov, E.; Amer, N.M.; Koren, G.
1989-01-01
Two novel flux creep related phenomena in YBa 2 Cu 3 O 7 - gd films are presented: a sharp onset of nonequilibrium optical response and a thermally activated electrical resistivity with logarithmic current dependence of the activation energy. This nonlinear current dependence is significantly different from the predictions of standard flux creep model
Creep feeding nursing beef calves.
Lardy, Gregory P; Maddock, Travis D
2007-03-01
Creep feeding can be used to increase calf weaning weights. However, the gain efficiency of free-choice, energy-based creep feeds is relatively poor. Generally, limit-feeding, high-protein creep feeds are more efficient, and gains may be similar to those produced by creep feeds offered free choice. Creep feeding can increase total organic matter intake and improve the overall energy status of the animal. Creep-fed calves tend to acclimate to the feedlot more smoothly than unsupplemented calves. Furthermore, provision of a high-starch creep feed may have a positive influence on subsequent carcass quality traits. Creep feeding can be applied to numerous environmental situations to maximize calf performance; however, beef cattle producers should consider their individual situations carefully before making the decision to creep feed.
Directory of Open Access Journals (Sweden)
Adailton S. Borges
Full Text Available Abstract A broad class of engineering systems can be satisfactory modeled under the assumptions of small deformations and linear material properties. However, many mechanical systems used in modern applications, like structural elements typical of aerospace and petroleum industries, have been characterized by increased slenderness and high static and dynamic loads. In such situations, it becomes indispensable to consider the nonlinear geometric effects and/or material nonlinear behavior. At the same time, in many cases involving dynamic loads, there comes the need for attenuation of vibration levels. In this context, this paper describes the development and validation of numerical models of viscoelastic slender beam-like structures undergoing large displacements. The numerical approach is based on the combination of the nonlinear Cosserat beam theory and a viscoelastic model based on Fractional Derivatives. Such combination enables to derive nonlinear equations of motion that, upon finite element discretization, can be used for predicting the dynamic behavior of the structure in the time domain, accounting for geometric nonlinearity and viscoelastic damping. The modeling methodology is illustrated and validated by numerical simulations, the results of which are compared to others available in the literature.
Neilson, Peter D; Neilson, Megan D
2005-09-01
Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships. AMT offers a unified account of how the nervous system might achieve these solutions by forming internal models. This is presented as the design of a simulator consisting of neural adaptive filters based on cerebellar circuitry. It incorporates a new network module that adaptively models (in real time) nonlinear relationships between inputs with changing and uncertain spectral and amplitude probability density functions as is the case for sensory and motor signals.
Drucker-Prager-Cap creep modelling of pebble beds in fusion blankets
International Nuclear Information System (INIS)
Hofer, D.; Kamlah, M.
2005-01-01
Modelling of thermal and mechanical behaviour of pebble beds for fusion blankets is an important issue to understand the interaction of solid breeder and beryllium pebble beds with the surrounding structural material. Especially the differing coefficients of thermal expansion of these materials cause high stresses and strains during irradiation induced volumetric heating. To describe this process, the coupled thermomechanical behaviour of both pebble bed materials has to be modelled. Additionally, creep has to be considered contributing to bed deformations and stress relaxation. Motivated by experiments, we use a continuum mechanical approach called Drucker-Prager/Cap theory to model the macroscopic pebble bed behaviour. The model accounts for pressure dependent shear failure, inelastic hardening, and volumetric creep. The elastic part is described by a nonlinear elasticity law. The model has been implemented by user-defined routines in the commercial finite-element code ABAQUS. To check the numerics, the implementation is compared to an analytical solution. Furthermore, the Drucker-Prager/Cap tool is applied to a single ceramic breeder bed subject to creep under volumetric heating
Creep deformations of shells of revolution under asymmetrical loading
International Nuclear Information System (INIS)
Takezono, S.
1975-01-01
The numerical analysis of creep deformations of shells of revolution under unsymmetrical loads is described with application to a cylindrical shell. The analytical formulation of the creep of axisymmetric undergoing unsymmetrical deformations is developed for two hardening laws: the time hardening law and the strain hardening law. The method is based on the creep power law, and on the assumption of plane stress condition and the Euler-Bernoulli hypothesis used in the ordinary thin shell theory. The basic differential equations derived for incremental values with respect to time are numerically solved by a finite difference method and the solutions at any time are obtained by integration of the incremental values. In conclusion the computer programs are developed which can be used to predict the creep deformations of arbitrary axisymmetrical shells. As a numerical example the creep deformation of cylindrical shell of importance in practical use is treated, and the variations of displacements and internal forces with the lapse of time are discussed
International Nuclear Information System (INIS)
Krishan, S.
2007-01-01
The Stieltjes transform has been used in place of a more common Laplace transform to determine the time evolution of the self-consistent field (SCF) of an unmagnetized semi-infinite plasma, where the plasma electrons together with a primary and a low-density secondary electron beam move perpendicular to the boundary surface. The secondary beam is produced when the primary beam strikes the grid. Such a plasma system has been investigated by Griskey and Stanzel [M. C. Grisky and R. L. Stenzel, Phys. Rev. Lett. 82, 556 (1999)]. The physical phenomenon, observed in their experiment, has been named by them as ''secondary beam instability.'' The character of the instability observed in the experiment is not the same as predicted by the conventional treatments--the field amplitude does not grow with time. In the frequency spectrum, the theory predicts peak values in the amplitude of SCF at the plasma frequency of plasma and secondary beam electrons, decreasing above and below it. The Stieltjes transform for functions, growing exponentially in the long time limit, does not exist, while the Laplace transform technique gives only exponentially growing solutions. Therefore, it should be interesting to know the kind of solutions that an otherwise physically unstable plasma will yield. In the high-frequency limit, the plasma has been found to respond to any arbitrary frequency of the initial field differentiated only by the strength of the resulting SCF. The condition required for exponential growth in the conventional treatments, and the condition for maximum amplitude (with respect to frequency) in the present treatment, have been found to be the same. Nonlinear mode coupling between the modes excited by the plasma electrons and the low-density secondary beam gives rise to two frequency-dependent peaks in the field amplitude, symmetrically located about the much stronger peak due to the plasma electrons, as predicted by the experiment
International Nuclear Information System (INIS)
Tarasov, V.A.; Borikov, T.L.; Kryzhanovskaya, T.V.; Chernezhenko, S.A.; Rusov, V.D.
2007-01-01
The kinetic system for defects of physical nonlinear system 'metal + load + irradiation' is specified [1, 2, 3]. Developing the approaches offered in [4], where distinctions of mechanisms of radiating creep and areas of their applicability are formalized (depending on external parameters) for fuel and constructional metals, division of kinetic systems for defects of constructional and fuel metals is carrying out. Thus the accent on the autocatalytic features of kinetic system for defects of reactor fuel metals, resulting from the exoenergic autocatalytic character of nuclear fission reactions being the main point defect source is done. In this part of the article the basic attention is given to the kinetic of sink drains for point defects. For kinetic systems of sinks-sources new approaches for the task of boundary conditions are offered. The possible structure of the computer program modelling kinetic system for defects of nonlinear physical system 'metal + load + irradiation' is considered
Multiaxial creep of tubes of Alloy 800 and Alloy 617 at high temperature
International Nuclear Information System (INIS)
Penkalla, H.J.; Schubert, F.; Nickel, H.
1989-01-01
The deformation behaviour under multiaxial loading at temperature higher than 800 deg. C is strongly controlled by creep. For dimensioning and inelastic analysis the use of v. Mises theory and Norton's creep law for stationary creep are demonstrated for different combination of internal pressure and axial or torsional stress or strains. The experimental results are in satisfactory agreement with the theoretical predicted deformation behaviour if values for the coefficient k and n in Norton's creep law are used, which are close to the real creep resistance in the component. (author). 11 refs, 12 figs, 2 tabs
Energy Technology Data Exchange (ETDEWEB)
Klimachkov, D. A., E-mail: klimchakovdmitry@gmail.com; Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru [Russian Academy of Sciences, Space Research Institute (Russian Federation)
2016-09-15
Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the
Study of the creep of lime-stabilised zirconia
International Nuclear Information System (INIS)
Saint-Jacques, Robert G.
1971-09-01
This research thesis reports the study of creep of stabilised zirconia containing between 13 and 20 per cent of lime, at temperatures between 1.200 and 1.400 C, and under compression stresses between 500 and 4.000 pounds by square inch. Specimens are polycrystalline with an average grain diameter between 7 and 29 microns. The author notably shows that the creep rate of lime-stabilised zirconia is directly proportional to the applied stress, and that the creep apparent activation energy is close to activation energy of volume self-diffusion of calcium and zirconium in lime-stabilised zirconia. Results of creep tests show that, in the studied conditions, the creep rate is directly proportional to the inverse of the grain average diameter, and this is in compliance with the Gifkins and Snowden theory of creep by sliding at grain boundaries. The author also shows that the creep rate of the lime stabilised zirconia varies with lime content, and reaches a maximum when zirconia contains about 15 per cent of lime. Lower creep rates obtained for higher and lower lime contents are explained [fr
Creep mechanisms and constitutive relations in pure metals
International Nuclear Information System (INIS)
Nix, W.D.
1979-01-01
The mechanisms of creep of pure metals is briefly reviewed and divided into two parts: steady state flow mechanisms, and non-steady state flow mechanisms and constitutive relations. Creep by diffusional flow is now reasonably well understood, with theory and experiment in good agreement. The closely related phenomenon of Harper--Dorn creep can also be understood in terms of diffusion between dislocations. Power law creep involves the climb of edge disloctions controlled by lattice self diffusion. Theoretical treatments of this process invariably give a power law exponent of 3. This natural creep law is compared with the data for FCC and BCC metals. It is suggested that diffusion controlled climb is the controlling process in BCC metals at very high temperatures. Stacking fault energy effects may preclude the possibility that creep is controlled entirely by lattice self diffusion in some FCC metals. The subject of power law breakdown is presented as a natural consequence of the transition to low temperature flow phenomena. The role of core diffusion in this transition is briefly discussed. The mechanisms are presented by which pure metals creep at elevated temperatures. While most of this review deals with the mechanisms of steady state flow, some discussion is devoted to creep flow under non-steady state conditions. This topic is discussed in connection with the development of constitutive equations for describing plastic flow in metals
International Nuclear Information System (INIS)
Yao, Jianyong; Jiao, Zongxia; Yao, Bin
2014-01-01
High performance robust force control of hydraulic load simulator with constant but unknown hydraulic parameters is considered. In contrast to the linear control based on hydraulic linearization equations, hydraulic inherent nonlinear properties and uncertainties make the conventional feedback proportional-integral-derivative (PID) control not yield to high performance requirements. Furthermore, the hydraulic system may be subjected to non-smooth and discontinuous nonlinearities due to the directional change of valve opening. In this paper, based on a nonlinear system model of hydraulic load simulator, a discontinuous projection-based nonlinear adaptive robust back stepping controller is developed with servo valve dynamics. The proposed controller constructs a novel stable adaptive controller and adaptation laws with additional pressure dynamic related unknown parameters, which can compensate for the system nonlinearities and uncertain parameters, meanwhile a well-designed robust controller is also synthesized to dominate the model uncertainties coming from both parametric uncertainties and uncertain nonlinearities including unmodeled and ignored system dynamics. The controller theoretically guarantee a prescribed transient performance and final tracking accuracy in presence of both parametric uncertainties and uncertain nonlinearities; while achieving asymptotic output tracking in the absence of unstructured uncertainties. The implementation issues are also discussed for controller simplification. Some comparative results are obtained to verify the high-performance nature of the proposed controller.
Energy Technology Data Exchange (ETDEWEB)
Yao, Jianyong [Nanjing University of Science and Technology, Nanjing (China); Jiao, Zongxia [Beihang University, Beijing (China); Yao, Bin [Purdue University, West Lafayette (United States)
2014-04-15
High performance robust force control of hydraulic load simulator with constant but unknown hydraulic parameters is considered. In contrast to the linear control based on hydraulic linearization equations, hydraulic inherent nonlinear properties and uncertainties make the conventional feedback proportional-integral-derivative (PID) control not yield to high performance requirements. Furthermore, the hydraulic system may be subjected to non-smooth and discontinuous nonlinearities due to the directional change of valve opening. In this paper, based on a nonlinear system model of hydraulic load simulator, a discontinuous projection-based nonlinear adaptive robust back stepping controller is developed with servo valve dynamics. The proposed controller constructs a novel stable adaptive controller and adaptation laws with additional pressure dynamic related unknown parameters, which can compensate for the system nonlinearities and uncertain parameters, meanwhile a well-designed robust controller is also synthesized to dominate the model uncertainties coming from both parametric uncertainties and uncertain nonlinearities including unmodeled and ignored system dynamics. The controller theoretically guarantee a prescribed transient performance and final tracking accuracy in presence of both parametric uncertainties and uncertain nonlinearities; while achieving asymptotic output tracking in the absence of unstructured uncertainties. The implementation issues are also discussed for controller simplification. Some comparative results are obtained to verify the high-performance nature of the proposed controller.
Creep consolidation of nuclear depository backfill materials
International Nuclear Information System (INIS)
Butcher, B.M.
1980-10-01
Evaluation of the effects of backfilling nuclear waste repository rooms is an important aspect of waste repository design. Consolidation of the porous backfill takes place as the room closes with time, causing the supporting stress exerted by the backfill against the intact rock to increase. Estimation of the rate of backfill consolidation is required for closure rate predictions and should be possible if the creep law for the solid constituent is known. A simple theory describing consolidation with a spherical void model is derived to illustrate this relationship. Although the present form of the theory assumes a homogeneous isotropic incompressible material atypical of most rocks, it may be applicable to rock salt, which exhibits considerable plasticity under confined pressure. Application of the theory is illustrated assuming a simple steady-state creep law, to show that the consolidation rate depends on the externally applied stress, temperature, and porosity
Enhanced aeroelastic energy harvesting by exploiting combined nonlinearities: theory and experiment
International Nuclear Information System (INIS)
Sousa, V C; De M Anicézio, M; De Marqui Jr, C; Erturk, A
2011-01-01
Converting aeroelastic vibrations into electricity for low power generation has received growing attention over the past few years. In addition to potential applications for aerospace structures, the goal is to develop alternative and scalable configurations for wind energy harvesting to use in wireless electronic systems. This paper presents modeling and experiments of aeroelastic energy harvesting using piezoelectric transduction with a focus on exploiting combined nonlinearities. An airfoil with plunge and pitch degrees of freedom (DOF) is investigated. Piezoelectric coupling is introduced to the plunge DOF while nonlinearities are introduced through the pitch DOF. A state-space model is presented and employed for the simulations of the piezoaeroelastic generator. A two-state approximation to Theodorsen aerodynamics is used in order to determine the unsteady aerodynamic loads. Three case studies are presented. First the interaction between piezoelectric power generation and linear aeroelastic behavior of a typical section is investigated for a set of resistive loads. Model predictions are compared to experimental data obtained from the wind tunnel tests at the flutter boundary. In the second case study, free play nonlinearity is added to the pitch DOF and it is shown that nonlinear limit-cycle oscillations can be obtained not only above but also below the linear flutter speed. The experimental results are successfully predicted by the model simulations. Finally, the combination of cubic hardening stiffness and free play nonlinearities is considered in the pitch DOF. The nonlinear piezoaeroelastic response is investigated for different values of the nonlinear-to-linear stiffness ratio. The free play nonlinearity reduces the cut-in speed while the hardening stiffness helps in obtaining persistent oscillations of acceptable amplitude over a wider range of airflow speeds. Such nonlinearities can be introduced to aeroelastic energy harvesters (exploiting
Study on creep behavior of Grade 91 heat-resistant steel using theta projection method
Ren, Facai; Tang, Xiaoying
2017-10-01
Creep behavior of Grade 91 heat-resistant steel used for steam cooler was characterized using the theta projection method. Creep tests were conducted at the temperature of 923K under the stress ranging from 100-150MPa. Based on the creep curve results, four theta parameters were established using a nonlinear least square fitting method. Four theta parameters showed a good linearity as a function of stress. The predicted curves coincided well with the experimental data and creep curves were also modeled to the low stress level of 60MPa.
DEFF Research Database (Denmark)
Stroescu, Ionut Emanuel; Sørensen, Lasse; Frigaard, Peter Bak
2016-01-01
A non-linear stretching method was implemented for stream function theory to solve wave kinematics for physical conditions close to breaking waves in shallow waters, with wave heights limited by the water depth. The non-linear stretching method proves itself robust, efficient and fast, showing good...
Theory of nonlinear interaction of particles and waves in an inverse plasma maser. Part 1
International Nuclear Information System (INIS)
Krivitsky, V.S.; Vladimirov, S.V.
1991-01-01
An expression is obtained for the collision integral describing the simultaneous interaction of plasma particles with resonant and non-resonant waves. It is shown that this collision integral is determined by two processes: a 'direct' nonlinear interaction of particles and waves, and the influence of the non-stationary of the system. The expression for the nonlinear collision integral is found to be quite different from the expression for a quasi-linear collision integral; in particular, the nonlinear integral contains higher-order derivatives of the distribution function with respect to momentum than the quasi-linear one. (author)
Theory and analysis of nonlinear dynamics and stability in storage rings: A working group summary
International Nuclear Information System (INIS)
Chattopadhyay, S.; Audy, P.; Courant, E.D.
1988-07-01
A summary and commentary of the available theoretical and analytical tools and recent advances in the nonlinear dynamics, stability and aperture issues in storage rings are presented. 11 refs., 4 figs
Stability of the static solitons in a pure spinor theory with fractional power nonlinearities
International Nuclear Information System (INIS)
Akdeniz, K.G.; Tezgor, G.; Barut, A.O.; Kalayci, J.; Okan, S.E.
1988-08-01
Soliton solutions are obtained in a pure fermionic model with fractional power nonlinear self-interactions. The stability properties of the minimum solutions have also been investigated within the framework of the Shatah-Strauss formalism. (author). 10 refs
Non-linear analytic and coanalytic problems (Lp-theory, Clifford analysis, examples)
International Nuclear Information System (INIS)
Dubinskii, Yu A; Osipenko, A S
2000-01-01
Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the 'orthogonal' sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented
Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)
Dubinskii, Yu A.; Osipenko, A. S.
2000-02-01
Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.
Stability analysis of nonlinear autonomous systems - General theory and application to flutter
Smith, L. L.; Morino, L.
1975-01-01
The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).
Density nonlinearities and a field theory for the dynamics of simple fluids
Mazenko, Gene F.; Yeo, Joonhyun
1994-01-01
We study the role of the Jacobian arising from a constraint enforcing the nonlinear relation: ${\\bf g}=\\rho{\\bf V}$, where $\\rho,\\: {\\bf g}$ and ${\\bf V}$ are the mass density, the momentum density and the local velocity field, respectively, in the field theoretic formulation of the nonlinear fluctuating hydrodynamics of simple fluids. By investigating the Jacobian directly and by developing a field theoretic formulation without the constraint, we find that no changes in dynamics result as co...
Micro creep mechanisms of tungsten
International Nuclear Information System (INIS)
Levoy, R.; Hugon, I.; Burlet, H.; Baillin, X.; Guetaz, L.
2000-01-01
Due to its high melting point (3410 deg C), tungsten offers good mechanical properties at elevated temperatures for several applications in non-oxidizing environment. The creep behavior of tungsten is well known between 1200 and 2500 deg C and 10 -3 to 10 -1 strain. However, in some applications when dimensional stability of components is required, these strains are excessive and it is necessary to know the creep behavior of the material for micro-strains (between 10 -4 and 10 -6 ). Methods and devices used to measure creep micro-strains are presented, and creep equations (Norton and Chaboche laws) were developed for wrought, annealed and recrystallized tungsten. The main results obtained on tungsten under low stresses are: stress exponent 1, symmetry of micro-strains in creep-tension and creep-compression, inverse creep (threshold stress), etc. TEM, SEM and EBSD studies allow interpretation of the micro-creep mechanism of tungsten under low stresses and low temperature (∼0.3 K) like the Harper-Dorn creep. In Harper-Dorn creep, micro-strains are associated with the density and the distribution of dislocations existing in the crystals before creep. At 975 deg C, the initial dislocation structure moves differently whether or not a stress is applied. To improve the micro-creep behavior of tungsten, a heat treatment is proposed to create the optimum dislocation structure. (authors)
Directory of Open Access Journals (Sweden)
Hamid M. Sedighi
Full Text Available This paper investigates the dynamic pull-in instability of vibrating micro-beams undergoing large deflection under electrosatically actuation. The governing equation of motion is derived based on the modified couple stress theory. Homotopy Perturbation Method is employed to produce the high accuracy approximate solution as well as the second-order frequency- amplitude relationship. The nonlinear governing equation of micro beam vibrations predeformed by an electric field includes both even and odd nonlinearities. The influences of basic non-dimensional parameters on the pull-in instability as well as the natural frequency are studied. It is demonstrated that two terms in series expansions are sufficient to produce high accuracy solution of the micro-structure. The accuracy of proposed asymptotic approach is validated via numerical results. The phase portrait of the system exhibits periodic and homoclinic orbits.
Directory of Open Access Journals (Sweden)
Weiwei Sun
2015-01-01
Full Text Available This paper presents H∞ excitation control design problem for power systems with input time delay and disturbances by using nonlinear Hamiltonian system theory. The impact of time delays introduced by remote signal transmission and processing in wide-area measurement system (WAMS is well considered. Meanwhile, the systems under investigation are disturbed by random fluctuation. First, under prefeedback technique, the power systems are described as a nonlinear Hamiltonian system. Then the H∞ excitation controller of generators connected to distant power systems with time delay and stochasticity is designed. Based on Lyapunov functional method, some sufficient conditions are proposed to guarantee the rationality and validity of the proposed control law. The closed-loop systems under the control law are asymptotically stable in mean square independent of the time delay. And we through a simulation of a two-machine power system prove the effectiveness of the results proposed in this paper.
Consistent creep and rupture properties for creep-fatigue evaluation
International Nuclear Information System (INIS)
Schultz, C.C.
1978-01-01
The currently accepted practice of using inconsistent representations of creep and rupture behaviors in the prediction of creep-fatigue life is shown to introduce a factor of safety beyond that specified in current ASME Code design rules for 304 stainless steel Class 1 nuclear components. Accurate predictions of creep-fatigue life for uniaxial tests on a given heat of material are obtained by using creep and rupture properties for that same heat of material. The use of a consistent representation of creep and rupture properties for a mininum strength heat is also shown to provide adequate predictions. The viability of using consistent properties (either actual or those of a minimum heat) to predict creep-fatigue life thus identifies significant design uses for the results of characterization tests and improved creep and rupture correlations
Consistent creep and rupture properties for creep-fatigue evaluation
International Nuclear Information System (INIS)
Schultz, C.C.
1979-01-01
The currently accepted practice of using inconsistent representations of creep and rupture behaviors in the prediction of creep-fatigue life is shown to introduce a factor of safety beyond that specified in current ASME Code design rules for 304 stainless steel Class 1 nuclear components. Accurate predictions of creep-fatigue life for uniaxial tests on a given heat of material are obtained by using creep and rupture properties for that same heat of material. The use of a consistent representation of creep and rupture properties for a minimum strength heat is also shown to provide reasonable predictions. The viability of using consistent properties (either actual or those of a minimum strength heat) to predict creep-fatigue life thus identifies significant design uses for the results of characterization tests and improved creep and rupture correlations. 12 refs
Contribution of dislocation creep to the radiational creep of materials
International Nuclear Information System (INIS)
Borodin, V.A.; Ryazanov, A.I.
1986-01-01
The authors propose a model of the orientational dependences of the preferences of discrete linear dislocations in which the influence of the external load on the step concentration at the dislocations is taken into account. The use of this model, taking into account the mechanism of stress-induced anisotropy of the elastic interaction between point defects and dislocations, not only permits a correct qualitative explanation of the dependence of the rate of radiational creep on the basic irradiation parameters (dose, stress, temperature) but also allows approximate quantitative agreement with experimental results to be obtained. At sufficiently high stress, the theory predicts conditions of the formation of an ensemble of dislocational loops with a specific direction of the Burgers vector
Experimental study on creep-fatigue interaction behavior of GH4133B superalloy
International Nuclear Information System (INIS)
Hu Dianyin; Wang Rongqiao
2009-01-01
The creep-fatigue tests have been conducted with nickel-based superalloy GH4133B at 600 deg. C in three cases of type loading to study the creep-fatigue behavior of the alloy and the loading history effect on the creep-fatigue damage. Since the conventional linear cumulative damage rule failed in evaluating the creep-fatigue life based on experimental data, a continuous non-linear model proposed by Mao et al. was employed to describe the creep-fatigue interaction. The creep-fatigue damage in the cases of continuous cyclic creep loading (CF) and prior fatigue followed by creep loading (F + C) was larger than unity and smaller than unity when the type loading was prior creep followed by fatigue loading (C + F). Scanning electron microscope (SEM) analyses of the fracture surface showed that the cracks initiated from the specimen surface and the fracture modes in different loading history were different. The crack mode at CF loading depended on the cyclic period. In the case of F + C loading, the primary fracture mode was transgranular, and in the condition where the type of waveform was C + F, the fracture mode was of mixed transgranular and intergranular type. In addition, the origin of the history effect on creep-fatigue interaction was explained by the SEM observations.
Nonlinear evolution of the matter power spectrum in modified theories of gravity
International Nuclear Information System (INIS)
Koyama, Kazuya; Taruya, Atsushi; Hiramatsu, Takashi
2009-01-01
We present a formalism to calculate the nonlinear matter power spectrum in modified gravity models that explain the late-time acceleration of the Universe without dark energy. Any successful modified gravity models should contain a mechanism to recover general relativity (GR) on small scales in order to avoid the stringent constrains on deviations from GR at solar system scales. Based on our formalism, the quasi-nonlinear power spectrum in the Dvali-Gabadadze-Porratti braneworld models and f(R) gravity models are derived by taking into account the mechanism to recover GR properly. We also extrapolate our predictions to fully nonlinear scales using the parametrized post-Friedmann framework. In the Dvali-Gabadadze-Porratti and f(R) gravity models, the predicted nonlinear power spectrum is shown to reproduce N-body results. We find that the mechanism to recover GR suppresses the difference between the modified gravity models and dark energy models with the same expansion history, but the difference remains large at the weakly nonlinear regime in these models. Our formalism is applicable to a wide variety of modified gravity models and it is ready to use once consistent models for modified gravity are developed.
Van de Kuilen, J.W.G.
2008-01-01
A creep analysis has been performed on nailed, toothed-plates and split-ring joints in a varying uncontrolled climate. The load levels varied between 30% and 50% of the average ultimate short term strength of these joints, tested in accordance with ISO 6891. The climate in which the tests were
Don S. Stone; Joseph E. Jakes; Jonathan Puthoff; Abdelmageed A. Elmustafa
2010-01-01
Finite element analysis is used to simulate cone indentation creep in materials across a wide range of hardness, strain rate sensitivity, and work-hardening exponent. Modeling reveals that the commonly held assumption of the hardness strain rate sensitivity (mΗ) equaling the flow stress strain rate sensitivity (mσ...
SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis
Energy Technology Data Exchange (ETDEWEB)
Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.
1998-08-01
This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. The notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.
Some New Results in Astrophysical Problems of Nonlinear Theory of Radiative Transfer
Pikichyan, H. V.
2017-07-01
In the interpretation of the observed astrophysical spectra, a decisive role is related to nonlinear problems of radiative transfer, because the processes of multiple interactions of matter of cosmic medium with the exciting intense radiation ubiquitously occur in astrophysical objects, and in their vicinities. Whereas, the intensity of the exciting radiation changes the physical properties of the original medium, and itself was modified, simultaneously, in a self-consistent manner under its influence. In the present report, we show that the consistent application of the principle of invariance in the nonlinear problem of bilateral external illumination of a scattering/absorbing one-dimensional anisotropic medium of finite geometrical thickness allows for simplifications that were previously considered as a prerogative only of linear problems. The nonlinear problem is analyzed through the three methods of the principle of invariance: (i) an adding of layers, (ii) its limiting form, described by differential equations of invariant imbedding, and (iii) a transition to the, so-called, functional equations of the "Ambartsumyan's complete invariance". Thereby, as an alternative to the Boltzmann equation, a new type of equations, so-called "kinetic equations of equivalence", are obtained. By the introduction of new functions - the so-called "linear images" of solution of nonlinear problem of radiative transfer, the linear structure of the solution of the nonlinear problem under study is further revealed. Linear images allow to convert naturally the statistical characteristics of random walk of a "single quantum" or their "beam of unit intensity", as well as widely known "probabilistic interpretation of phenomena of transfer", to the field of nonlinear problems. The structure of the equations obtained for determination of linear images is typical of linear problems.
Creep buckling of shell structures
International Nuclear Information System (INIS)
Miyazaki, Noriyuki; Hagihara, Seiya
2015-01-01
The present article contains a review of the literatures on the creep buckling of shell structures published from late 1950's to recent years. In this article, the creep buckling studies on circular cylindrical shells, spherical shells, partial cylindrical shells and other shells are reviewed in addition to creep buckling criteria. Creep buckling is categorized into two types. One is the creep buckling due to quasi-static instability, in which the critical time for creep buckling is determined by tracing a creep deformation versus time curve. The other is the creep buckling due to kinetic instability, in which the critical time can be determined by examining the shape of total potential energy in the vicinity of a quasi-static equilibrium state. Bifurcation buckling and snap-through buckling during creep deformation belong to this type of creep buckling. A few detailed descriptions are given to the bifurcation and snap-through type of creep buckling based on the present authors' works. (author)
Nonlinear Analysis of Rotors Supported by Air Foil Journal Bearings – Theory and Experiments
DEFF Research Database (Denmark)
Larsen, Jon Steffen
with a good margin of rotordynamical stable operation. To ensure this, good mathematical models, capable of accurately predicting the dynamic behaviour of the rotor-bearing system, are required at the design stage. This thesis focuses on developing and improving existing mathematical models for predicting...... mechanical behaviour of the bump foils was carefully examined. A mathematical model capable of predicting this nonlinear behaviour was developed and compared to the experimental results with good agreement. With the second test rig, the overall nonlinear behaviour of the rotor-bearing system was investigated...
Strength and life under creeping
International Nuclear Information System (INIS)
Pospishil, B.
1982-01-01
Certain examples of the application of the Lepin modified creep model, which are of interest from technical viewpoint, are presented. Mathematical solution of the dependence of strength limit at elevated temperatures on creep characteristics is obtained. Tensile test at elevated temperatures is a particular case of creep or relaxation and both strength limit and conventional yield strength at elevated temperatures are completely determined by parameters of state equations during creep. The equation of fracture summing during creep is confirmed not only by the experiment data when stresses change sporadically, but also by good reflection of durability curve using the system of equations. The system presented on the basis of parameters of the equations obtained on any part of durability curve, permits to forecast the following parameters of creep: strain, strain rate, life time, strain in the process of fracture. Tensile test at elevated temperature is advisable as an addition when determining creep curves (time-strain curves) [ru
Plasticity - a limiting case of creep
International Nuclear Information System (INIS)
Cords, H.; Kleist, G.; Zimmermann, R.
1986-11-01
The present work is an attempt to develop further the so-called unified theory for viscoplastic constitutive equations as used for metals or metal alloys. Typically, in similar approaches creep strains and plastic strains are derived from one common stress-strain relationship for inelastic strain rates employing an internal stress function as a back stress. Some novel concepts concerning the definition of the internal stress, plastic yielding and material hardening have been introduced, formulated mathematically and tested for correspondence with a standard type of materials behaviour. As a result of the investigations a system of simultaneous differential equations is defined which has been used to elaborate a common view on a number of different material effects observed in creep and plasticity i.e. normal and inverted primary creep, recoverable creep, incubation time and anelasticity in stress reduction, negative stress relaxation, plastic yielding, perfect plasticity, negative strain rate sensitivity, serrated flow, strain hardening in monotonic and cyclic loading. The theoretical approach is mainly based on a lateral contraction movement not following rigidly the longitudinal extension of the material specimen by a prescribed constant value of Poisson's ratio as usual, but following the axial extension in a process of drag which allows for retardation and which simultaneously impedes the longitudinal straining. (orig.) [de
National Research Council Canada - National Science Library
Drazin, P. G
1992-01-01
This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...
Demonstration of creep during filtration
DEFF Research Database (Denmark)
Christensen, Morten Lykkegaard; Bugge, Thomas Vistisen; Kirchheiner, Anders Løvenbalk
The classical filtration theory assumes a unique relationship between the local filter cake porosity and the local effective pressure. For a number of compressible materials, it has however been observed that during the consolidation stage this may not be the case. It has been found...... that the production of filtrate also depends on the characteristic time for the filter cake solids to deform. This is formulated in the Terzaghi-Voigt model in which a secondary consolidation is introduced. The secondary consolidation may be visualized by plots of the relative cake deformation (U) v.s. the square...... root of time. Even more clearly it is demonstrated by plotting the liquid pressure at the cake piston interface v.s. the relative deformation (to be shown). The phenomenon of a secondary consolidation processes is in short called creep. Provided that the secondary consolidation rate is of the same...
Creep behaviour and creep mechanisms of normal and healing ligaments
Thornton, Gail Marilyn
Patients with knee ligament injuries often undergo ligament reconstructions to restore joint stability and, potentially, abate osteoarthritis. Careful literature review suggests that in 10% to 40% of these patients the graft tissue "stretches out". Some graft elongation is likely due to creep (increased elongation of tissue under repeated or sustained load). Quantifying creep behaviour and identifying creep mechanisms in both normal and healing ligaments is important for finding clinically relevant means to prevent creep. Ligament creep was accurately predicted using a novel yet simple structural model that incorporated both collagen fibre recruitment and fibre creep. Using the inverse stress relaxation function to model fibre creep in conjunction with fibre recruitment produced a superior prediction of ligament creep than that obtained from the inverse stress relaxation function alone. This implied mechanistic role of fibre recruitment during creep was supported using a new approach to quantify crimp patterns at stresses in the toe region (increasing stiffness) and linear region (constant stiffness) of the stress-strain curve. Ligament creep was relatively insensitive to increases in stress in the toe region; however, creep strain increased significantly when tested at the linear region stress. Concomitantly, fibre recruitment was evident at the toe region stresses; however, recruitment was limited at the linear region stress. Elevating the water content of normal ligament using phosphate buffered saline increased the creep response. Therefore, both water content and fibre recruitment are important mechanistic factors involved in creep of normal ligaments. Ligament scars had inferior creep behaviour compared to normal ligaments even after 14 weeks. In addition to inferior collagen properties affecting fibre recruitment and increased water content, increased glycosaminoglycan content and flaws in scar tissue were implicated as potential mechanisms of scar creep
International Nuclear Information System (INIS)
Schröck, Johannes; Meurer, Thomas; Kugi, Andreas
2011-01-01
This paper considers a flexible cantilever beam, which is actuated by piezoelectric macro-fiber composite (MFC) patch actuators. For accurate positioning tasks, special attention has to be paid to the inherent nonlinear hysteresis and creep behavior of these actuators. A detailed analysis of the MFC-actuated cantilever verifies that these nonlinearities can be efficiently captured by an operator-based model using Prandtl–Ishlinskii's theory. Based on a Hammerstein-like model with the nonlinearities at the input connected in series with a linear infinite-dimensional beam model it follows that hysteresis and creep effects can be compensated by application of the inverse operator. Experimental results prove the feasibility of this approach. With this result, the tracking accuracy of the combination of the compensator with the flatness-based feedforward control design as proposed in the companion paper (Schröck et al 2011 Smart Mater. Struct. 20 015015) can be verified. Measurements demonstrate the applicability of this approach for the realization of highly dynamic trajectories for the beam's tip deflection
Relation between linear and nonlinear N=3,4 supergravity theories
International Nuclear Information System (INIS)
Sevrin, A.; Thielemans, K.; Troost, W.
1993-01-01
The effective actions for d=2, N=3,4 chiral supergravities with a linear and a nonlinear gauge algebra are related to each other by a quantum reduction; the latter is obtained from the former by putting quantum currents equal to zero. This implies that the renormalization factors for the quantum actions are identical
Knoester, Jasper; Mukamel, Shaul
1990-01-01
A general scheme is presented for calculating the nonlinear optical response in condensed phases that provides a unified picture of excitons, polaritons, retardation, and local-field effects in crystals and in disordered systems. A fully microscopic starting point is taken by considering the
Kinetic theory of nonlinear viscous flow in two and three dimensions
Ernst, M.H.; Cichocki, B.; Dorfman, J.R.; Sharma, J.; Beijeren, H. van
1978-01-01
On the basis of a nonlinear kinetic equation for a moderately dense system of hard spheres and disks it is shown that shear and normal stresses in a steady-state, uniform shear flow contain singular contributions of the form ¦X¦3/2 for hard spheres, or ¦X¦ log ¦X¦ for hard disks. HereX is
Directory of Open Access Journals (Sweden)
Milovanović Branislav
2007-01-01
Full Text Available Introduction: There are different proofs about association of autonomic nervous system dysfunction, especially nonlinear parameters, with higher mortality after myocardial infarction. Objective The objective of the study was to determine predictive value of Poincare plot as nonlinear parameter and other significant standard risk predictors: ejection fraction of the left ventricle, late potentials, ventricular arrhythmias, and QT interval. Method The study included 1081 patients with mean follow up of 28 months (ranging fom 0-80 months. End-point of the study was cardiovascular mortality. The following diagnostic methods were used during the second week: ECG with commercial software Schiller AT-10: short time spectral analysis of RR variability with analysis of Poincare plot as nonlinear parameter and late potentials; 24-hour ambulatory ECG monitoring: QT interval, RR interval, QT/RR slope, ventricular arrhythmias (Lown >II; echocardiography examinations: systolic disorder (defined as EF<40 %. Results There were 103 (9.52% cardiovascular deaths during the follow-up. In univariate analysis, the following parameters were significantly correlated with mortality: mean RR interval < 800 ms, QT and RR interval space relationship as mean RR interval < 800 ms and QT interval > 350 ms, positive late potentials, systolic dysfunction, Poincare plot as a point, ventricular arrhythmias (Lown > II. In multivariate analysis, the significant risk predictors were: Poincare plot as a point and mean RR interval lower than 800 ms. Conclusion Mean RR interval lower than 800 ms and nonlinear and space presentation of RR interval as a point Poincare plot were multivariate risk predictors.
International Nuclear Information System (INIS)
Esmaeilzadeh Khadem, S.; Rezaee, M.
2001-01-01
In this paper the large amplitude and non-linear vibration of a string is considered. The initial tension, lateral vibration amplitude, diameter and the modulus of elasticity of the string have main effects on its natural frequencies. Increasing the lateral vibration amplitude makes the assumption of constant initial tension invalid. In this case, therefore, it is impossible to use the classical equation of string with small amplitude transverse motion assumption. On the other hand, by increasing the string diameter, the bending moment effect will increase dramatically, and acts as an impressive restoring moment. Considering the effects of the bending moments, the nonlinear equation governing the large amplitude transverse vibration of a string is derived. The time dependent portion of the governing equation has the from of Duff ing equation is solved using the perturbation theory. The results of the analysis are shown in appropriate graphs, and the natural frequencies of the string due to the non-linear factors are compared with the natural frequencies of the linear vibration os a string without bending moment effects
Osherovich, V. A.; Fainberg, J.
2018-01-01
We consider simultaneous oscillations of electrons moving both along the axis of symmetry and also in the direction perpendicular to the axis. We derive a system of three nonlinear ordinary differential equations which describe self-similar oscillations of cold electrons in a constant proton density background (np = n0 = constant). These three equations represent an exact class of solutions. For weak nonlinear conditions, the frequency spectra of electric field oscillations exhibit split frequency behavior at the Langmuir frequency ωp0 and its harmonics, as well as presence of difference frequencies at low spectral values. For strong nonlinear conditions, the spectra contain peaks at frequencies with values ωp0(n +m √{2 }) , where n and m are integer numbers (positive and negative). We predict that both spectral types (weak and strong) should be observed in plasmas where axial symmetry may exist. To illustrate possible applications of our theory, we present a spectrum of electric field oscillations observed in situ in the solar wind by the WAVES experiment on the Wind spacecraft during the passage of a type III solar radio burst.
Goldman, Benjamin D.; Scott, Robert C,; Dowell, Earl H.
2014-01-01
The purpose of this work is to develop a set of theoretical and experimental techniques to characterize the aeroelasticity of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). A square TPS coupon experiences trailing edge oscillatory behavior during experimental testing in the 8' High Temperature Tunnel (HTT), which may indicate the presence of aeroelastic flutter. Several theoretical aeroelastic models have been developed, each corresponding to a different experimental test configuration. Von Karman large deflection theory is used for the plate-like components of the TPS, along with piston theory for the aerodynamics. The constraints between the individual TPS layers and the presence of a unidirectional foundation at the back of the coupon are included by developing the necessary energy expressions and using the Rayleigh Ritz method to derive the nonlinear equations of motion. Free vibrations and limit cycle oscillations are computed and the frequencies and amplitudes are compared with accelerometer and photogrammetry data from the experiments.
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Creep and creep-rupture behavior of Alloy 718
International Nuclear Information System (INIS)
Brinkman, C.R.; Booker, M.K.; Ding, J.L.
1991-01-01
Data obtained from creep and creep-rupture tests conducted on 18 heats of Alloy 718 were used to formulate models for predicting high temperature time dependent behavior of this alloy. Creep tests were conducted on specimens taken from a number of commercial product forms including plate, bar, and forgoing material that had been procured and heat treated in accordance with ASTM specifications B-670 or B-637. Data were obtained over the temperature range of 427 to 760 degree C ad at test times to about 87,000 h. Comparisons are given between experimental data and the analytical models. The analytical models for creep-rupture included one based on lot-centering regression analysis and two based on the Minimum Commitment Method. A ''master'' curve approach was used to develop and equation for estimating creep deformation up to the onset of tertiary creep. 11 refs., 13 figs
Description of Concrete Creep under Time-Varying Stress Using Parallel Creep Curve
Park, Yeong-Seong; Lee, Yong-Hak; Lee, Youngwhan
2016-01-01
An incremental format of creep model was presented to take account of the development of concrete creep due to loading at different ages. The formulation was attained by introducing a horizontal parallel assumption of creep curves and combining it with the vertical parallel creep curve of the rate of creep method to remedy the disadvantage of the rate of creep method that significantly underestimates the amount of creep strain, regardless of its simple format. Two creep curves were combined b...
Evaluation of specific heat for superfluid helium between 0 - 2.1 K based on nonlinear theory
International Nuclear Information System (INIS)
Sasaki, Shosuke
2009-01-01
The specific heat of liquid helium was calculated theoretically in the Landau theory. The results deviate from experimental data in the temperature region of 1.3 - 2.1 K. Many theorists subsequently improved the results of the Landau theory by applying temperature dependence of the elementary excitation energy. As well known, many-body system has a total energy of Galilean covariant form. Therefore, the total energy of liquid helium has a nonlinear form for the number distribution function. The function form can be determined using the excitation energy at zero temperature and the latent heat per helium atom at zero temperature. The nonlinear form produces new temperature dependence for the excitation energy from Bose condensate. We evaluate the specific heat using iteration method. The calculation results of the second iteration show good agreement with the experimental data in the temperature region of 0 - 2.1 K, where we have only used the elementary excitation energy at 1.1 K.
International Nuclear Information System (INIS)
Holland, C.; Kim, E.J.; Champeaux, S.; Gurcan, O.; Rosenbluth, M.N.; Diamond, P.H.; Tynan, G.R.; Nevins, W.; Candy, J.
2003-01-01
Understanding the physics of shear flow and structure formation in plasmas is a central problem for the advancement of magnetic fusion because of the roles such flows are believed to play in regulating turbulence and transport levels. In this paper, we report on integrated experimental, computational, and theoretical studies of sheared zonal flows and radially extended convective cells, with the aim of assessing the results of theory experiment and theory-simulation comparisons. In particular, simulations are used as test beds for verifying analytical predictions and demonstrating the suitability of techniques such as bispectral analysis for isolating nonlinear couplings in data. Based on intriguing initial results suggesting increased levels of nonlinear coupling occur during L-H transitions, we have undertaken a comprehensive study of bispectral quantities in fluid and gyrokinetic simulations, and compared these results with theoretical expectations. Topics of study include locality and directionality of energy transfer, amplitude scaling, and parameter dependences. Techniques for inferring nonlinear coupling coefficients from data are discussed, and initial results from experimental data are presented. Future experimental studies are motivated. We also present work investigating the role of structures in transport. Analysis of simulation data indicates that the turbulent heat flux can be represented as an ensemble of 'heat pulses' of varying sizes, with a power law distribution. The slope of the power law is shown to determine global transport scaling (i.e. Bohm or gyro-Bohm). Theoretical work studying the dynamics of the largest cells (termed 'streamers') is presented, as well as results from ongoing analysis studying connections between heat pulse distribution and bispectral quantities. (author)
SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics
Energy Technology Data Exchange (ETDEWEB)
Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.
1999-03-01
This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.
Fuchs, Armin
2013-01-01
With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified.This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz ...
A New Monotone Iteration Principle in the Theory of Nonlinear Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2015-08-01
Full Text Available In this paper the author proves the algorithms for the existence as well as approximations of the solutions for the initial value problems of nonlinear fractional diﬀerential equations using the operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid ﬁxed point theorems of Dhage (2014 in a partially ordered normed linear space and the existence and approximations of the solutions of the considered nonlinear fractional diﬀerential equations are obtained under weak mixed partial continuity and partial Lipschitz conditions. Our hypotheses and existence and approximation results are also well illustrated by some numerical examples.
Theory of nonlinear harmonic generation in free-electron lasers with helical wigglers
International Nuclear Information System (INIS)
Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.
2007-05-01
CoherentHarmonicGeneration (CHG), and in particularNonlinearHarmonicGeneration (NHG), is of importance for both short wavelength Free-Electron Lasers (FELs), in relation with the achievement of shorter wavelengths with a fixed electron-beam energy, and high-average power FEL resonators, in relation with destructive effects of higher harmonics radiation on mirrors. In this paper we present a treatment of NHG from helical wigglers with particular emphasis on the second harmonic. Our study is based on an exact analytical solution of Maxwell's equations, derived with the help of a Green's function method. In particular, we demonstrate that nonlinear harmonic generation (NHG) fromhelicalwigglers vanishes on axis. Our conclusion is in open contrast with results in literature, that include a kinematical mistake in the description of the electron motion. (orig.)
A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials
Li, Chen; Liao, Yufei
2018-03-01
Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.
Emergence of complex space-temporal order in nonlinear field theories
International Nuclear Information System (INIS)
Gleiser, Marcelo
2006-01-01
We investigate the emergence of time-dependent nonperturbative configurations during the evolution of nonlinear scalar field models with symmetric and asymmetric double-well potentials. Complex space-temporal behavior emerges as the system seeks to establish equipartition after a fast quench. We show that fast quenches may dramatically modify the decay rate of metastable states in first order phase transitions. We discuss possible applications in condensed matter systems and in inflationary cosmology. (author)
Emergence of Complex Spatio-Temporal Behavior in Nonlinear Field Theories
International Nuclear Information System (INIS)
Gleiser, Marcelo; Howell, Rafael C.
2006-01-01
We investigate the emergence of time-dependent nonperturbative configurations during the evolution of nonlinear scalar field models with symmetric and asymmetric double-well potentials. Complex spatio-temporal behavior emerges as the system seeks to establish equipartition after a fast quench. We show that fast quenches may dramatically modify the decay rate of metastable states in first order phase transitions. We discuss possible applications in condensed matter systems and early universe cosmology
Simulation of irradiation creep
International Nuclear Information System (INIS)
Reiley, T.C.; Jung, P.
1977-01-01
The results to date in the area of radiation enhanced deformation using beams of light ions to simulate fast neutron displacement damage are reviewed. A comparison is made between these results and those of in-reactor experiments. Particular attention is given to the displacement rate calculations for light ions and the electronic energy losses and their effect on the displacement cross section. Differences in the displacement processes for light ions and neutrons which may effect the irradiation creep process are discussed. The experimental constraints and potential problem areas associated with these experiments are compared to the advantages of simulation. Support experiments on the effect of thickness on thermal creep are presented. A brief description of the experiments in progress is presented for the following laboratories: HEDL, NRL, ORNL, PNL, U. of Lowell/MIT in the United States, AERE Harwell in the United Kingdom, CEN Saclay in France, GRK Karlsruhe and KFA Julich in West Germany
International Nuclear Information System (INIS)
Charnock, W.; Cordwell, J.E.
1978-03-01
Available information on the creep of austenitic, ferritic and Alloy-800 type steels in liquid sodium is critically reviewed. Creep properties of stainless steels can be affected by element transfer and corrosion. At reactor structural component temperatures environmental effects are likely to be less important than changes due to thermal ageing. At high clad temperatures (700 0 C) decarburisation may cause the loss of strength and ductility in unstabilised steels while cavity formation may cause embrittlement in stabilised steels. The properties of Alloy 800 are, in some experiments, found to deteriorate while in others they are enhanced. This may be a consequence of the metallurgical complexity of the material or arise from the nature of the various techniques employed. Low alloy ferritic steels tend to decarburise in sodium at temperatures greater than 500 0 C and this leads to loss of strength and an increase in ductility. High alloy ferritics are immune to this effect and appear to be able to tolerate a degree of carburisation. Although intergranular cracking may be enhanced in liquid sodium the mechanical consequences are not significant and evidence for the existence of an embrittlement effect not associated with element transfer or corrosion is weak. Stress and strain may enhance element transfer at crack tips. However in real cracks the gettering or supply action of the crack faces conditions the chemistry of the cracks in sodium and protects the crack tip from element transfer. Thus creep crack extension rates should be independent of changes in bulk coolant chemistry. (author)
High temperature creep of vanadium
International Nuclear Information System (INIS)
Juhasz, A.; Kovacs, I.
1978-01-01
The creep behaviour of polycrystalline vanadium of 99.7% purity has been investigated in the temperature range 790-880 0 C in a high temperature microscope. It was found that the creep properties depend strongly on the history of the sample. To take this fact into account some additional properties such as the dependence of the yield stress and the microhardness on the pre-annealing treatment have also been studied. Samples used in creep measurements were selected on the basis of their microhardness. The activation energy of creep depends on the microhardness and on the creep temperature. In samples annealed at 1250 0 C for one hour (HV=160 kgf mm -2 ) the rate of creep is controlled by vacancy diffusion in the temperature range 820-880 0 C with an activation energy of 78+-8 kcal mol -1 . (Auth.)
Creep of fibrous composite materials
DEFF Research Database (Denmark)
Lilholt, Hans
1985-01-01
Models are presented for the creep behaviour of fibrous composite materials with aligned fibres. The models comprise both cases where the fibres remain rigid in a creeping matrix and cases where the fibres are creeping in a creeping matrix. The treatment allows for several contributions...... to the creep strength of composites. The advantage of combined analyses of several data sets is emphasized and illustrated for some experimental data. The analyses show that it is possible to derive creep equations for the (in situ) properties of the fibres. The experiments treated include model systems...... such as Ni + W-fibres, high temperature materials such as Ni + Ni3Al + Cr3C2-fibres, and medium temperature materials such as Al + SiC-fibres. For the first two systems reasonable consistency is found for the models and the experiments, while for the third system too many unquantified parameters exist...
Numerical algorithms in secondary creep
International Nuclear Information System (INIS)
Feijoo, R.A.; Taroco, E.
1980-01-01
The problem of stationary creep is presented as well as its variational formulation, when weak constraints are established, capable of assuring one single solution. A second, so-called elasto-creep problem, is further analysed, together with its variational formulation. It is shown that its stationary solution coincides with that of the stationary creep and the advantages of this formulation with respect to the former one is emphasized. Some numerical applications showing the efficiency of the method propesed are finally presented [pt
Creep analysis of orthotropic shells
International Nuclear Information System (INIS)
Mehra, V.K.; Ghosh, A.
1975-01-01
A method of creep analysis of orthotropic cylindrical shells subjected to axisymmetric loads has been developed. A general study of creep behaviour of cylindrical shells subjected to a uniform internal pressure has been conducted for a wide range of values of anisotropy coefficients and creep law exponent. Analysis includes determination of stress re-distribution, strain rates, stationary state stresses. Application of reference stress technique has been extended to analysis of shells. (author)
A nonlinear theory of cosmic ray pitch angle diffusion in homogeneous magnetostatic turbulence
International Nuclear Information System (INIS)
Goldstein, M.L.
1975-04-01
A plasma strong turbulence, weak coupling theory is applied to the problem of cosmic ray pitch angle scattering in magnetostatic turbulence. The theory used is a rigorous generalization of Weinstock's resonance-broadening theory and contains no ad hoc approximations. A detailed calculation is presented for a model of slab turbulence with an exponential correlation function. The results agree well with numerical simulations. The rigidity dependence of the pitch angle scattering coefficient differs from that found by previous researchers. The differences result from an inadequate treatment of particle trajectories near 90 0 pitch angle in earlier work
Thermal ratcheting and creep damage
International Nuclear Information System (INIS)
Clement, G.; Cousseran, P.; Roche, R.L.
1983-01-01
Several proposals have been made to assist adesigners with thermal ratcheting in the creep range, the more known has been made by O'DONNELL and POROWSKY. Unfortunately these methods are not validated by experiments, and they take only inelastic distortion into consideration as creep effects. The aim of the work presented here is to correct these deficiencies - in providing an experimental basis to ratcheting analysis rules in the creep range, - in considering the effect of cyclic straining (like cyclic thermal stresses) on the time to rupture by creep. Experimental tests have been performed on austenitic stainless steel at 650 0 C for the first item. Results of these tests and results available in the open literature have been used to built a practical rule of ratcheting analysis. This rule giving a conservative value of the creep distortion, is based on the concept of effective primary stress which is an amplification of the primary stress really applied. Concerning the second point (time to rupture), it was necessary to obtain real creep rupture and not instability. According to the proposal of Pr LECKIE, tests were performed on specimens made out of copper, and of aluminium alloys at temperatures between 150 0 C and 300 0 C. With such materials creep rupture is obtained without necking. Experimental tests show that cyclic straining reduces the time to creep rupture under load controlled stress. Caution must be given to the designer: cyclic thermal stress can lead to premature creep rupture. (orig./GL)
Creep of high temperature composites
International Nuclear Information System (INIS)
Sadananda, K.; Feng, C.R.
1993-01-01
High temperature creep deformation of composites is examined. Creep of composites depends on the interplay of many factors. One of the basic issues in the design of the creep resistant composites is the ability to predict their creep behavior from the knowledge of the creep behavior of the individual components. In this report, the existing theoretical models based on continuum mechanics principles are reviewed. These models are evaluated using extensive experimental data on molydisilicide-silicon carbide composites obtained by the authors. The analysis shows that the rule of mixture based on isostrain and isostress provides two limiting bounds wherein all other theoretical predictions fall. For molydisilicide composites, the creep is predominantly governed by the creep of the majority phase, i.e. the matrix with fibers deforming elastically. The role of back stresses both on creep rates and activation energies are shown to be minimum. Kinetics of creep in MoSi 2 is shown to be controlled by the process of dislocation glide with climb involving the diffusion of Mo atoms
Radiation-induced creep and swelling
International Nuclear Information System (INIS)
Heald, P.T.
1977-01-01
The physical basis for radiation induced creep and swelling is reviewed. The interactions between the point defects and dislocations are recalled since these interactions are ultimately responsible for the observable deformation phenomena. Both the size misfit interaction and the induced inhomogeneity interaction are considered since the former gives rise to irradiation swelling while the latter, which depends on both internal and external stresses, results in irradiation creep. The defect kinetics leading to the deformation processes are discussed in terms of chemical rate theory. The rate equations for the spatially averaged interstitial and vacancy concentrations are expressed in terms of the microstructural sink strengths and the solution of these equations leads to general expressions for the deformation rates
Transient effects in friction fractal asperity creep
Goedecke, Andreas
2013-01-01
Transient friction effects determine the behavior of a wide class of mechatronic systems. Classic examples are squealing brakes, stiction in robotic arms, or stick-slip in linear drives. To properly design and understand mechatronic systems of this type, good quantitative models of transient friction effects are of primary interest. The theory developed in this book approaches this problem bottom-up, by deriving the behavior of macroscopic friction surfaces from the microscopic surface physics. The model is based on two assumptions: First, rough surfaces are inherently fractal, exhibiting roughness on a wide range of scales. Second, transient friction effects are caused by creep enlargement of the real area of contact between two bodies. This work demonstrates the results of extensive Finite Element analyses of the creep behavior of surface asperities, and proposes a generalized multi-scale area iteration for calculating the time-dependent real contact between two bodies. The toolset is then demonstrated both...
Creep failure of a spray drier
CSIR Research Space (South Africa)
Carter, P
1998-06-01
Full Text Available , and creep. The calculations pointed to creep, and no positive metallurgic or physical evidence was discovered to support any of the hypotheses. However, the compression stresses implied that creep deformation could have occurred without inducing discernible...
Theory of heart biomechanics, biophysics, and nonlinear dynamics of cardiac function
Hunter, Peter; McCulloch, Andrew
1991-01-01
In recent years there has been a growth in interest in studying the heart from the perspective of the physical sciences: mechanics, fluid flow, electromechanics. This volume is the result of a workshop held in July 1989 at the Institute for Nonlinear Sciences at the University of California at San Diego that brought together scientists and clinicians with graduate students and postdoctoral fellows who shared an interest in the heart. The chapters were prepared by the invited speakers as didactic reviews of their subjects but also include the structure, mechanical properties, and function of the heart and the myocardium, electrical activity of the heart and myocardium, and mathematical models of heart function.
Reactor noise analysis based on nonlinear dynamic theory - application to power oscillation
International Nuclear Information System (INIS)
Suzudo, Tomoaki
1993-01-01
The information dimension is one of the simplest quantities that can be used to determine the asymptotic motion of the time evolution of a nonlinear system. The application of this quantity to reactor noise analysis is proposed, and the possibility of its application to power oscillation analysis is examined. The information dimension of this regime is equal to the number of independent oscillating modes, which is an intuitive physical variable. Time series data from computer experiments and experiments with an actual physical system are used for the analysis. The results indicate that the method is useful for a detailed analysis of reactor power oscillation
Properties of Energy Spectra of Molecular Crystals Investigated by Nonlinear Theory
Pang, Xiao-Feng; Zhang, Huai-Wu
We calculate the quantum energy spectra of molecular crystals, such as acetanilide, by using discrete nonlinear Schrodinger equation, containing various interactions, appropriate to the systems. The energy spectra consist of many energy bands, in each energy band there are a lot of energy levels including some higher excited states. The result of energy spectrum is basically consistent with experimental values obtained by infrared absorption and Raman scattering in acetanilide and can also explain some experimental results obtained by Careri et al. Finally, we further discuss the influences of variously characteristic parameters on the energy spectra of the systems.
Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman Operator Theory
2017-03-01
Koopman operator theory to systems with memory in time made during Year 1, during Year 2 we worked toward developing a test capable of determining...using this term. Approved for public release; distribution is unlimited. 6 Furthermore, a key element of an approach that is fully capable of dealing...Operator Theory by Bryan Glaz and Adam Svenkeson Approved for public release; distribution is unlimited. NOTICES
Nonlinear behavior of capacitive micro-beams based on strain gradient theory
International Nuclear Information System (INIS)
Fathalilou, Mohammad; Sadeghi, Morteza; Rezazadeh, Ghader
2014-01-01
This paper studies the size dependent behavior of materials in MEMS structures. This behavior becomes noticeable for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter and is insignificant for the high ratio of the characteristic size to the length-scale parameter, which is the case of the silicon base micro-beams. However, in some types of micro-beams like gold or nickel bases, the size dependent effect cannot be overlooked. In such cases, ignoring this behavior in modeling will lead to incorrect results. Some previous researchers have applied classic beam theory on their models and imposed a considerable hypothetical value of residual stress to match their theoretical results with the experimental ones. The equilibrium positions or fixed points of the gold and nickel micro-beams are obtained and shown that for a given DC voltage, there is a considerable difference between the obtained fixed points using classic beam theory, modified couple stress theory, and modified strain gradient theory. In addition, it is shown that the calculated static and dynamic pull-in voltages using higher order theories are much closer to the experimental results and are higher several times than those obtained by classic beam theory.
International Nuclear Information System (INIS)
Barhen, J.; Bjerke, M.A.; Cacuci, D.G.; Mullins, C.B.; Wagschal, G.G.
1982-01-01
An advanced methodology for performing systematic uncertainty analysis of time-dependent nonlinear systems is presented. This methodology includes a capability for reducing uncertainties in system parameters and responses by using Bayesian inference techniques to consistently combine prior knowledge with additional experimental information. The determination of best estimates for the system parameters, for the responses, and for their respective covariances is treated as a time-dependent constrained minimization problem. Three alternative formalisms for solving this problem are developed. The two ''off-line'' formalisms, with and without ''foresight'' characteristics, require the generation of a complete sensitivity data base prior to performing the uncertainty analysis. The ''online'' formalism, in which uncertainty analysis is performed interactively with the system analysis code, is best suited for treatment of large-scale highly nonlinear time-dependent problems. This methodology is applied to the uncertainty analysis of a transient upflow of a high pressure water heat transfer experiment. For comparison, an uncertainty analysis using sensitivities computed by standard response surface techniques is also performed. The results of the analysis indicate the following. Major reduction of the discrepancies in the calculation/experiment ratios is achieved by using the new methodology. Incorporation of in-bundle measurements in the uncertainty analysis significantly reduces system uncertainties. Accuracy of sensitivities generated by response-surface techniques should be carefully assessed prior to using them as a basis for uncertainty analyses of transient reactor safety problems
Control theory-based regulation of hippocampal CA1 nonlinear dynamics.
Hsiao, Min-Chi; Song, Dong; Berger, Theodore W
2008-01-01
We are developing a biomimetic electronic neural prosthesis to replace regions of the hippocampal brain area that have been damaged by disease or insult. Our previous study has shown that the VLSI implementation of a CA3 nonlinear dynamic model can functionally replace the CA3 subregion of the hippocampal slice. As a result, the propagation of temporal patterns of activity from DG-->VLSI-->CA1 reproduces the activity observed experimentally in the biological DG-->CA3-->CA1 circuit. In this project, we incorporate an open-loop controller to optimize the output (CA1) response. Specifically, we seek to optimize the stimulation signal to CA1 using a predictive dentate gyrus (DG)-CA1 nonlinear model (i.e., DG-CA1 trajectory model) and a CA1 input-output model (i.e., CA1 plant model), such that the ultimate CA1 response (i.e., desired output) can be first predicted by the DG-CA1 trajectory model and then transformed to the desired stimulation through the inversed CA1 plant model. Lastly, the desired CA1 output is evoked by the estimated optimal stimulation. This study will be the first stage of formulating an integrated modeling-control strategy for the hippocampal neural prosthetic system.
Nonlinear power spectrum from resummed perturbation theory: a leap beyond the BAO scale
International Nuclear Information System (INIS)
Anselmi, Stefano; Pietroni, Massimo
2012-01-01
A new computational scheme for the nonlinear cosmological matter power spectrum (PS) is presented. Our method is based on evolution equations in time, which can be cast in a form extremely convenient for fast numerical evaluations. A nonlinear PS is obtained in a time comparable to that needed for a simple 1-loop computation, and the numerical implementation is very simple. Our results agree with N-body simulations at the percent level in the BAO range of scales, and at the few-percent level up to k ≅ 1 h/Mpc at z∼>0.5, thereby opening the possibility of applying this tool to scales interesting for weak lensing. We clarify the approximations inherent to this approach as well as its relations to previous ones, such as the Time Renormalization Group, and the multi-point propagator expansion. We discuss possible lines of improvements of the method and its intrinsic limitations by multi streaming at small scales and low redshifts
Phase-space description of plasma waves. Linear and nonlinear theory
International Nuclear Information System (INIS)
Biro, T.
1992-11-01
We develop an (r,k) phase space description of waves in plasmas by introducing Gaussian window functions to separate short scale oscillations from long scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation also in an inhomogeneous and time varying background plasma, we first discuss the proper form of the current response function. On the analogy of the particle distribution function f(v,r,t), we introduce a wave density N(k,r,t) on phase space. This function is proven to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density' along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible. Within the phase space representation, we obtain a very general formula for the second order nonlinear current in terms of the vector potential. This formula is a convenient starting point for studies of coherent as well as turbulent nonlinear processes. We derive kinetic equations for weakly inhomogeneous and turbulent plasma, including the effects of inhomogeneous turbulence, wave convection and refraction. (author)
Stress Distribution in Layered Elastic Creeping Array with a Vertical Cylindrical Shaft
Directory of Open Access Journals (Sweden)
Bobyleva Tatiana
2017-01-01
Full Text Available Construction should be taking into account the influence of time factor on the stability of the structures. In the paper hereditary creep and homogenization theories are used to determine stresses in the layered elastic creeping array with a vertical shaft. Volterra correspondence principle was applied. As a result, the reduction of a time-dependent elastic creeping problem to a corresponding elastic problem became possible. The method proposes a way to determine average (effective elastic creeping properties and homogenized stress field from known properties of the layers’ components. Creep kernels are of a convolution type and are taken in the exponential form. The problem of heterogeneous elastic creeping environment is reduced to a problem of homogeneous transversely isotropic medium. Different boundary conditions on the cylindrical shaft’s surface were considered. An analytical solution was obtained. These explicit expressions can be useful for the necessary calculations in the construction practice.
Louisnard, O
2012-01-01
The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. A correct estimation of the wave attenuation in such bubbly media requires a realistic estimation of the power dissipated by the oscillation of each bubble, by thermal diffusion in the gas and viscous friction in the liquid. Both quantities and calculated numerically for a single inertial bubble driven at 20 kHz, and are found to be several orders of magnitude larger than the linear prediction. Viscous dissipation is found to be the predominant cause of energy loss for bubbles small enough. Then, the classical nonlinear Caflish equations describing the propagation of acoustic waves in a bubbly liquid are recast and simplified conveniently. The main harmonic part of the sound field is found to fulfill a nonlinear Helmholtz equation, where the imaginary part of the squared wave number is directly correlated with the energy lost by a single bubble. For low acoustic driving, linear theory is recovered, but for larger drivings, namely above the Blake threshold, the attenuation coefficient is found to be more than 3 orders of magnitude larger then the linear prediction. A huge attenuation of the wave is thus expected in regions where inertial bubbles are present, which is confirmed by numerical simulations of the nonlinear Helmholtz equation in a 1D standing wave configuration. The expected strong attenuation is not only observed but furthermore, the examination of the phase between the pressure field and its gradient clearly demonstrates that a traveling wave appears in the medium. Copyright © 2011 Elsevier B.V. All rights reserved.
LDRD final report on theory and exploration of quantum-dot optical nonlinearities and coherences
International Nuclear Information System (INIS)
Chow, Weng Wah
2008-01-01
A microscopic theory for investigating quantum-dot optical properties was developed. The theory incorporated advances on various aspects of quantum-dot physics developed at Sandia and elsewhere. Important components are a non-Markovian treatment of polarization dephasing due to carrier-carrier scattering (developed at Sandia) and a nonperturbative treatment within a polaron picture of the scattering of carriers by longitudinal-optical phonons (developed at Bremen University). A computer code was also developed that provides a detailed accounting of electronic structure influences and a consistent treatment of many-body effects, the latter via the incorporation of results from the microscopic theory. This code was used to explore quantum coherence physics in a quantum-dot system. The investigation furthers the understanding of the underlying differences between atomic quantum coherence and semiconductor quantum coherence, and helps improve the potential of using quantum coherences in quantum computing, coherent control and high-resolution spectroscopy
On the use of contraction theory for the design of nonlinear observers for ocean vehicles
DEFF Research Database (Denmark)
Jouffroy, Jerome; Lottin, Jacques
and practice. This paper addresses the question of the applicability of contraction theory to the design of UGES observers for ocean vehicles. A relation between the concept of exponential convergence of a contracting system and uniform global exponential stability (UGES) is rst given. Then two contraction......Guaranteeing that traditional concepts of stability like uniform global exponential or asymptotic stability (UGES or UGAS) are veri ed when using design tools based on new concepts of stability may be of signicant importance. It is especially so when attempting to bridge the gap between theory...
Nucleon-nucleon scattering in the functional quantum theory of the non-linear spinor field
International Nuclear Information System (INIS)
Philipp, W.
1975-01-01
The nucleon-nucleon and nucleon-antinucleon scattering cross sections are calculated in the frame of the functional quantum field theory by means of two different approximation methods: averaging by integration of indefinite integrals and pulse averaging. The results for nucleon-nucleon scattering are compared with experimental data, with calculations using a modified functional scalar product and with results in first order perturbation theory (V-A-coupling). As for elastic nucleon-antinucleon scattering, the S matrix is investigated for crossing symmetry. Scattering of 'nucleons' of different mass results in different cross sections even in the lowest-order approximation. (BJ) [de
An experimental and theoretical investigation of creep buckling
International Nuclear Information System (INIS)
Ohya, H.
1977-01-01
The purpose of the present paper is to investigate creep buckling phenomena and the methods of analysis. Creep buckling experiments were performed on aluminum alloy 2024-T4 cylindrical shells having radius to thickness ratios of 16, 25, 50 and 80, in single, double and triple step axial compression at 250 0 C. It was observed that buckling occurred at one of the edges and the buckling mode depended on the radius to thickness ratio and also on the applied stress level. Thicker cylinders buckled in axisymmetric mode. Thinner ones under higher applied stress levels buckled in the asymmetric mode, whereas they under lower applied stress levels buckled in the axisymmetric mode. Creep buckling times were obtained from end shortening record of the cylinders. Experimental results were compared with theoretical values obtained by the following two methods. One is a simplified method to estimate buckling times, proposed by Gerard et al., Papirno et al. and others. The method is based on the fact that the creep buckling solutions are analogous to those of plastic buckling under a certain assumption. It was found that the bukling times could be reasonably estimated by this simplified method. The other is a finite element computer program for axisymmetric thin shells. This program is based on the incremental theory and can treat thermoelastoplastic creep analysis of axisymmetric thin shells with large deflection. Creep deformation behavior of cylindrical shells under axial compression and buckling times were calculated by the program and the effects of plasticity on buckling times were also investigated
International Nuclear Information System (INIS)
Maldonado, G.I.; Turinsky, P.J.; Kropaczek, D.J.
1993-01-01
The computational capability of efficiently and accurately evaluate reactor core attributes (i.e., k eff and power distributions as a function of cycle burnup) utilizing a second-order accurate advanced nodal Generalized Perturbation Theory (GPT) model has been developed. The GPT model is derived from the forward non-linear iterative Nodal Expansion Method (NEM) strategy, thereby extending its inherent savings in memory storage and high computational efficiency to also encompass GPT via the preservation of the finite-difference matrix structure. The above development was easily implemented into the existing coarse-mesh finite-difference GPT-based in-core fuel management optimization code FORMOSA-P, thus combining the proven robustness of its adaptive Simulated Annealing (SA) multiple-objective optimization algorithm with a high-fidelity NEM GPT neutronics model to produce a powerful computational tool used to generate families of near-optimum loading patterns for PWRs. (orig.)
Understanding the mechanisms of amorphous creep through molecular simulation.
Cao, Penghui; Short, Michael P; Yip, Sidney
2017-12-26
Molecular processes of creep in metallic glass thin films are simulated at experimental timescales using a metadynamics-based atomistic method. Space-time evolutions of the atomic strains and nonaffine atom displacements are analyzed to reveal details of the atomic-level deformation and flow processes of amorphous creep in response to stress and thermal activations. From the simulation results, resolved spatially on the nanoscale and temporally over time increments of fractions of a second, we derive a mechanistic explanation of the well-known variation of creep rate with stress. We also construct a deformation map delineating the predominant regimes of diffusional creep at low stress and high temperature and deformational creep at high stress. Our findings validate the relevance of two original models of the mechanisms of amorphous plasticity: one focusing on atomic diffusion via free volume and the other focusing on stress-induced shear deformation. These processes are found to be nonlinearly coupled through dynamically heterogeneous fluctuations that characterize the slow dynamics of systems out of equilibrium.
Knotted solutions for linear and nonlinear theories: Electromagnetism and fluid dynamics
Directory of Open Access Journals (Sweden)
Daniel W.F. Alves
2017-10-01
Full Text Available We examine knotted solutions, the most simple of which is the “Hopfion”, from the point of view of relations between electromagnetism and ideal fluid dynamics. A map between fluid dynamics and electromagnetism works for initial conditions or for linear perturbations, allowing us to find new knotted fluid solutions. Knotted solutions are also found to be solutions of nonlinear generalizations of electromagnetism, and of quantum-corrected actions for electromagnetism coupled to other modes. For null configurations, electromagnetism can be described as a null pressureless fluid, for which we can find solutions from the knotted solutions of electromagnetism. We also map them to solutions of Euler's equations, obtained from a type of nonrelativistic reduction of the relativistic fluid equations.
Phantom solution in a non-linear Israel-Stewart theory
Cruz, Miguel; Cruz, Norman; Lepe, Samuel
2017-06-01
In this paper we present a phantom solution with a big rip singularity in a non-linear regime of the Israel-Stewart formalism. In this framework it is possible to extend this causal formalism in order to describe accelerated expansion, where assumption of near equilibrium is no longer valid. We assume a flat universe filled with a single viscous fluid ruled by a barotropic EoS, p = ωρ, which can represent a late time accelerated phase of the cosmic evolution. The solution allows to cross the phantom divide without evoking an exotic matter fluid and the effective EoS parameter is always lesser than -1 and constant in time.
Creep Measurement Video Extensometer
Jaster, Mark; Vickerman, Mary; Padula, Santo, II; Juhas, John
2011-01-01
Understanding material behavior under load is critical to the efficient and accurate design of advanced aircraft and spacecraft. Technologies such as the one disclosed here allow accurate creep measurements to be taken automatically, reducing error. The goal was to develop a non-contact, automated system capable of capturing images that could subsequently be processed to obtain the strain characteristics of these materials during deformation, while maintaining adequate resolution to capture the true deformation response of the material. The measurement system comprises a high-resolution digital camera, computer, and software that work collectively to interpret the image.
Quantitive theory of the Fermi-Pasta-Ulam recurrence in the nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Infeld, E.
1981-01-01
By limiting attention to the lowest-order Fourier modes we obtain a theory of the Fermi-Pasta-Ulam recurrence that gives excellent agreement with recent numerical results. Both the predicted period of the recurrence and the temporal development of the n = 0 mode are very good fits. The maximum of the n = 1 mode, however, is off by about 30%
Using Nonlinear Programming in International Trade Theory: The Factor-Proportions Model
Gilbert, John
2004-01-01
Students at all levels benefit from a multi-faceted approach to learning abstract material. The most commonly used technique in teaching the pure theory of international trade is a combination of geometry and algebraic derivations. Numerical simulation can provide a valuable third support to these approaches. The author describes a simple…
DEFF Research Database (Denmark)
Bendtsen, Claus; Nielsen, Ole Holm; Hansen, Lars Bruno
2001-01-01
The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a self-consistent field (SCF) solution of large eigenvalue problems. The iterative Davidson algorithm is often used, and we...
Vortex pinning and creep experiments
International Nuclear Information System (INIS)
Kes, P.H.
1991-01-01
A brief review of basic flux-pinning and flux-creep ingredients and a selection of experimental results on high-temperature-superconductivity compounds is presented. Emphasis is put on recent results and on those properties which are central to the emerging understanding of the flux-pinning and flux-creep mechanisms of these fascinating materials
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
Probability based high temperature engineering creep and structural fire resistance
Razdolsky, Leo
2017-01-01
This volume on structural fire resistance is for aerospace, structural, and fire prevention engineers; architects, and educators. It bridges the gap between prescriptive- and performance-based methods and simplifies very complex and comprehensive computer analyses to the point that the structural fire resistance and high temperature creep deformations will have a simple, approximate analytical expression that can be used in structural analysis and design. The book emphasizes methods of the theory of engineering creep (stress-strain diagrams) and mathematical operations quite distinct from those of solid mechanics absent high-temperature creep deformations, in particular the classical theory of elasticity and structural engineering. Dr. Razdolsky’s previous books focused on methods of computing the ultimate structural design load to the different fire scenarios. The current work is devoted to the computing of the estimated ultimate resistance of the structure taking into account the effect of high temperatur...
Cairns, Iver H.; Robinson, P. A.
1998-01-01
Existing, competing theories for coronal and interplanetary type III solar radio bursts appeal to one or more of modulational instability, electrostatic (ES) decay processes, or stochastic growth physics to preserve the electron beam, limit the levels of Langmuir-like waves driven by the beam, and produce wave spectra capable of coupling nonlinearly to generate the observed radio emission. Theoretical constraints exist on the wavenumbers and relative sizes of the wave bandwidth and nonlinear growth rate for which Langmuir waves are subject to modulational instability and the parametric and random phase versions of ES decay. A constraint also exists on whether stochastic growth theory (SGT) is appropriate. These constraints are evaluated here using the beam, plasma, and wave properties (1) observed in specific interplanetary type III sources, (2) predicted nominally for the corona, and (3) predicted at heliocentric distances greater than a few solar radii by power-law models based on interplanetary observations. It is found that the Langmuir waves driven directly by the beam have wavenumbers that are almost always too large for modulational instability but are appropriate to ES decay. Even for waves scattered to lower wavenumbers (by ES decay, for instance), the wave bandwidths are predicted to be too large and the nonlinear growth rates too small for modulational instability to occur for the specific interplanetary events studied or the great majority of Langmuir wave packets in type III sources at arbitrary heliocentric distances. Possible exceptions are for very rare, unusually intense, narrowband wave packets, predominantly close to the Sun, and for the front portion of very fast beams traveling through unusually dilute, cold solar wind plasmas. Similar arguments demonstrate that the ES decay should proceed almost always as a random phase process rather than a parametric process, with similar exceptions. These results imply that it is extremely rare for
Thermal ratcheting and creep damage
International Nuclear Information System (INIS)
Clement, G.; Cousseran, P.; Roche, R.L.
1983-08-01
Creep is a cause of deformation; it may also result in rupture in time. Although LMFBR structures are not heavily loaded, they are subjected to large thermal transients. Can structure lifetime be shortened by such transients. Several proposals have been made to assist adesigners with thermal ratcheting in the creep range. Unfortunately these methods are not validated by experiments, and they take only inelastic distorsion into consideration as creep effects. The aim of the work presented here is to correct these deficiencies in providing an experimental basis to ratcheting analysis rules in the creep range, and in considering the effect of cyclic straining (like cyclic thermal stresses) on the time to rupture by creep. Experimental tests have been performed on austenitic stainless steel at 650 0 C for the first item. Results of these tests and results available in the open literature have been used to built a practical rule of ratcheting analysis. This rule giving a conservative value of the creep distortion, is based on the concept of effective primary stress which is an amplification of the primary stress really applied. Concerning the second point (time to rupture), it was necessary to obtain real creep rupture and not instability. According to the proposal of Pr LECKIE, tests were performed on specimen made out of copper, and of aluminium alloys at temperatures between 150 0 C and 300 0 C. With such materials creep rupture is obtained without necking. Experimental tests show that cyclic straining reduces the time to creep rupture under load controlled stress. Caution must be given to the designer: cyclic thermal stress can lead to premature creep rupture
Creep Deformation by Dislocation Movement in Waspaloy.
Whittaker, Mark; Harrison, Will; Deen, Christopher; Rae, Cathie; Williams, Steve
2017-01-12
Creep tests of the polycrystalline nickel alloy Waspaloy have been conducted at Swansea University, for varying stress conditions at 700 °C. Investigation through use of Transmission Electron Microscopy at Cambridge University has examined the dislocation networks formed under these conditions, with particular attention paid to comparing tests performed above and below the yield stress. This paper highlights how the dislocation structures vary throughout creep and proposes a dislocation mechanism theory for creep in Waspaloy. Activation energies are calculated through approaches developed in the use of the recently formulated Wilshire Equations, and are found to differ above and below the yield stress. Low activation energies are found to be related to dislocation interaction with γ' precipitates below the yield stress. However, significantly increased dislocation densities at stresses above yield cause an increase in the activation energy values as forest hardening becomes the primary mechanism controlling dislocation movement. It is proposed that the activation energy change is related to the stress increment provided by work hardening, as can be observed from Ti, Ni and steel results.
Meerson, Baruch; Fouxon, Itzhak; Vilenkin, Arkady
2008-02-01
We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes and employing Lagrangian coordinates, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation becomes exactly soluble, and the solution develops a finite-time density blowup. The blowup has the same local features at singularity as those exhibited by the recently found family of exact solutions of the full set of ideal hydrodynamic equations [I. Fouxon, Phys. Rev. E 75, 050301(R) (2007); I. Fouxon,Phys. Fluids 19, 093303 (2007)]. The heat diffusion, however, always becomes important near the attempted singularity. It arrests the density blowup and brings about previously unknown inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. The ICSs represent exact solutions of the full set of granular hydrodynamic equations. Both the density profile of an ICS and the characteristic relaxation time toward it are determined by a single dimensionless parameter L that describes the relative role of the inelastic energy loss and heat diffusion. At L>1 the intermediate cooling dynamics proceeds as a competition between "holes": low-density regions of the gas. This competition resembles Ostwald
Gravity Dual for Reggeon Field Theory and Non-linear Quantum Finance
Yu Nakayama
2009-01-01
We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the non-relativistic conformal invariance. We discuss applications to scaling regime of Reggeo...
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...
Hamilton-Ostrogradsky principle in the theory of nonlinear elasticity with the combined approach
International Nuclear Information System (INIS)
Sporykhin, A.N.
1995-01-01
The assignment of a portion of the edge conditions in the deformed state and a portion of them in the initial state so that the initial and deformed states of the body are unknowns is a characteristic feature of the statement of a number of technological problems. Haber and Haber and Abel have performed studies in this direction, where constitutive relationships have been constructed within the framework of a linearly elastic material. Use of the displacements of individual particles as variable parameters in these relationships has required additional conditions that do not follow from the formulated problem. Use of familiar variational principles described in Euler coordinates is rendered difficult by the complexity of edge-condition formulation in the special case when the initial state is unknown. The latter is governed by the fact that variational principles are derived from the initial formulations open-quotes in Lagrangian coordinates,close quotes by recalculating the operation functional. Using Lagrange's principle, Novikov and Sporykhin constructed constitutive equations in the general case of a nonlinearly elastic body with edge conditions assigned in different configurations. An analogous problem is solved in this paper using the Hamilton-Ostrogradsky principle
Detection of seizures from small samples using nonlinear dynamic system theory.
Yaylali, I; Koçak, H; Jayakar, P
1996-07-01
The electroencephalogram (EEG), like many other biological phenomena, is quite likely governed by nonlinear dynamics. Certain characteristics of the underlying dynamics have recently been quantified by computing the correlation dimensions (D2) of EEG time series data. In this paper, D2 of the unbiased autocovariance function of the scalp EEG data was used to detect electrographic seizure activity. Digital EEG data were acquired at a sampling rate of 200 Hz per channel and organized in continuous frames (duration 2.56 s, 512 data points). To increase the reliability of D2 computations with short duration data, raw EEG data were initially simplified using unbiased autocovariance analysis to highlight the periodic activity that is present during seizures. The D2 computation was then performed from the unbiased autocovariance function of each channel using the Grassberger-Procaccia method with Theiler's box-assisted correlation algorithm. Even with short duration data, this preprocessing proved to be computationally robust and displayed no significant sensitivity to implementation details such as the choices of embedding dimension and box size. The system successfully identified various types of seizures in clinical studies.
Theory for nonlinear magnetosonic waves in a two-ion-species plasma
International Nuclear Information System (INIS)
Toida, Mieko; Ohsawa, Yukiharu
1997-01-01
Magnetosonic waves propagating perpendicular to a magnetic field in a plasma containing two ion species is studied theoretically. The magnetosonic wave is split into two modes in a two-ion-species plasma; low- and high- frequency modes. The frequency of the low-frequency mode tends to zero as the wave number k goes to zero. A KdV equation is derived for this mode by the conventional reductive perturbation method. The frequency of high-frequency mode does not go to zero as k → 0. However, using a new expansion scheme, a KdV equation for the nonlinear high-frequency mode has also been derived. This shows that KdV equations are not limited to waves whose frequencies tend to zero as k → 0. The KdV equation for the low-frequency mode is valid when the amplitudes ε are quite small, while that for the high-frequency mode is valid when (m. e /m. i ) 1/2 e /m. i is a measure of electron-to-ion mass ratios. The characteristic soliton widths are the ion inertia length for the low-frequency mode and the electron skin depth for the high-frequency mode. (author)
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
Nonlinear dynamics of a pseudoelastic shape memory alloy system—theory and experiment
International Nuclear Information System (INIS)
Enemark, S; F Santos, I; A Savi, M
2014-01-01
In this work, a helical spring made from a pseudoelastic shape memory alloy was embedded in a dynamic system also composed of a mass, a linear spring and an excitation system. The mechanical behaviour of shape memory alloys is highly complex, involving hysteresis, which leads to damping capabilities and varying stiffness. Besides, these properties depend on the temperature and pretension conditions. Because of these capabilities, shape memory alloys are interesting in relation to engineering design of dynamic systems. A theoretical model based on a modification of the 1D Brinson model was established. Basically, the hardening and the sub-loop behaviour were altered. The model parameters were extracted from force–displacement tests of the spring at different constant temperatures as well as from differential scanning calorimetry. Model predictions were compared with experimental results of free and forced vibrations of the system setup under different temperature conditions. The experiments give a thorough insight into dynamic systems involving pseudoelastic shape memory alloys. Comparison between experimental results and the proposed model shows that the model is able to explain and predict the overall nonlinear behaviour of the system. (paper)
Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation
Directory of Open Access Journals (Sweden)
V. O. Vakhnenko
2016-01-01
Full Text Available A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE, by a change of independent variables. The VPE has an N-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprises N-loop-like solitons. Aspects of the inverse scattering transform (IST method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads to N-soliton solutions and M-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.
International Nuclear Information System (INIS)
Nelipa, N.F.
1978-01-01
The existence of the solution of the nonlinear, singular equations of quantum field theory is discussed. By making use of the Banach's and Schauder's fixed point theorems, the condition of the existence of these equations is found. As some illustration, these methods were applied to the equations for the π-scattering on static nucleon. The investigations of the other equations of quantum field theory (Chew-Low, double dispersin relation, Green's function) lead to the similar result. The application of the Newton-Kantorovich method to the Chew-Low equations also gives the similar result. What are the causes of such situation[ The main suggestions which the author has used were that the Banach's, the Schauder's, and the Newton-Kantorovich methods were applied and the Hoelder space was choosen. It may be that the method are crude. It may be that the solutions do not belong to the Hoelder space. Now it is rather difficult to say which role each of these two suggestions plays. (Kobatake, H.)
Non Newtonian gravity creeping flow
International Nuclear Information System (INIS)
Gratton, J.; Mahajan, S.M.; Minotti, F.
1988-11-01
We derive the governing equations for creeping gravity currents of non Newtonian liquids having a power law rheology, using a lubrication approximation. We consider unidirectional and axisymmetric currents. The equations differ from those for Newtonian liquids, being nonlinear in the spatial derivative of the thickness of the current. However, many solutions are closely analogous to those for Newtonian rheology; in particular the spreading relations can also be expressed as power laws of time, with exponents that depend on the rheological index. Similarity solutions for currents whose volume varies as a power of time are obtained. For the spread of a constant volume of liquid, analytic solutions are found. We also derive solutions of the waiting-time type, as well as the ones describing steady flows from a constant source to a sink. General travelling wave solutions are given, and analytic formulae for a simple case are derived. A phase plane formalism, that allows the systematic derivation of self similar solutions, is introduced. The application of the Boltzmann transform is briefly discussed. Present results are closely analogous to those for Newtonian liquids; all the solutions obtained here have their counterparts in Newtonian flows. This happens because the power law rheology, like the Newtonian constitutive relation, involves a single dimensional parameter. Thus one finds similarity solutions whenever the analogous Newtonian problem is self similar. Although the spreading relations are rheology-dependent, in most cases the dependence is rather weak. The present results may be of interest for geophysics since the lithosphere deforms according to an average power law rheology. (author). 17 refs
Zheligovsky, Vladislav
2011-01-01
New developments for hydrodynamical dynamo theory have been spurred by recent evidence of self-sustained dynamo activity in laboratory experiments with liquid metals. The emphasis in the present volume is on the introduction of powerful mathematical techniques required to tackle modern multiscale analysis of continous systems and there application to a number of realistic model geometries of increasing complexity. This introductory and self-contained research monograph summarizes the theoretical state-of-the-art to which the author has made pioneering contributions.
Exact solutions to nonlinear symmetron theory: One- and two-mirror systems
Brax, Philippe; Pitschmann, Mario
2018-03-01
We derive the exact analytical solutions to the symmetron field theory equations in the presence of a one- or two-mirror system. The one-dimensional equations of motion are integrated exactly for both systems and their solutions can be expressed in terms of Jacobi elliptic functions. Surprisingly, in the case of two parallel mirrors, the equations of motion generically provide not a unique solution but a discrete set of solutions with increasing number of nodes and energies. The solutions obtained herein can be applied to q BOUNCE experiments, neutron interferometry and for the calculation of the symmetron-field-induced "Casimir force" in the CANNEX experiment.
Negative creep in nickel base superalloys
DEFF Research Database (Denmark)
Dahl, Kristian Vinter; Hald, John
2004-01-01
Negative creep describes the time dependent contraction of a material as opposed to the elongation seen for a material experiencing normal creep behavior. Negative creep occurs because of solid state transformations that results in lattice contractions. For most applications negative creep will h...
Mechanisms of transient radiation-induced creep
International Nuclear Information System (INIS)
Pyatiletov, Yu.S.
1981-01-01
Radiation-induced creep at the transient stage is investigated for metals. The situation, when several possible creep mechanisms operate simultaneously is studied. Among them revealed are those which give the main contribution and determine thereby the creep behaviour. The time dependence of creep rate and its relation to the smelling rate is obtained. The results satisfactorily agree with the available experimental data [ru
Modeling Creep Processes in Aging Polymers
Olali, N. V.; Voitovich, L. V.; Zazimko, N. N.; Malezhik, M. P.
2016-03-01
The photoelastic method is generalized to creep in hereditary aging materials. Optical-creep curves and mechanical-creep or optical-relaxation curves are used to interpret fringe patterns. For materials with constant Poisson's ratio, it is sufficient to use mechanical- or optical-creep curves for this purpose
Examination of the creep behaviour of ceramic fuel elements under neutron irradiation
International Nuclear Information System (INIS)
Brucklacher, D.
1978-01-01
This paper examines the creeping of UO 2 , UO 2 -PuO 2 and UN under neutron irradiation. It starts with the experimental results about the relation between the thermal creep rate and the load, the temperature, as well as characteristic material values, stoichiometry, grain size and porosity. These correlation are first qualitatively discussed and then compared with the statements of actual quantitative equations. From the models and theories on which these equations are based a modified Nabarro-Heering-equation results for the correlation between the creep rate of ceramic fuels, stress, temperature and the fission rate. In the experimental part of the examination, length-changes of creep samples of UO 2 , (U,Pu)O 2 and UN were measured in specially developed irradiation creep casings in different reactors. The measuring data were corrected and evaluated considering the thermal expansion effects, irregular temperature distribution and swelling effects in such a way that the dependences of the creep rate of UO 2 , UO 2 -PuO 2 and UN under irradiation on stress, temperature, fission rate, burn-up and porosity is obtained. It shows that creeping of fuels under irradiation at high temperatures is equivalent to thermally activated creeping, while at low temperature the creep rate induced by irradiation is much higher than the condition without irradiation. The increment of oxidic nuclear fuels is greater than in UN, the stress dependence on low burn-up is proportional in both cases, and the influence of temperature is quite small. (orig.) [de
Creep constitutive equation of dual phase 9Cr-ODS steel
International Nuclear Information System (INIS)
Sakasegawa, Hideo; Ukai, Shigeharu; Tamura, Manabu; Ohtsuka, Satoshi; Tanigawa, Hiroyasu; Ogiwara, Hiroyuki; Kohyama, Akira; Fujiwara, Masayuki
2008-01-01
9Cr-ODS (oxide dispersion strengthened) steels developed by JAEA (Japan Atomic Energy Agency) have superior creep properties compared with conventional heat resistant steels. The ODS steels can enormously contribute to practical applications of fast breeder reactors and more attractive fusion reactors. Key issues are developments of material processing procedures for mass production and creep life prediction methods in present R and D. In this study, formulation of creep constitutive equation was performed against the backdrop. The 9Cr-ODS steel displaying an excellent creep property is a dual phase steel. The ODS steel is strengthened by the δ ferrite which has a finer dispersion of oxide particles and shows a higher hardness than the α' martensite. The δ ferrite functions as a reinforcement in the dual phase 9Cr-ODS steel. Its creep behavior is very unique and cannot be interpreted by conventional theories of heat resistant steels. Alternative qualitative model of creep mechanism was formulated at the start of this study using the results of microstructural observations. Based on the alternative creep mechanism model, a novel creep constitutive equation was formulated using the exponential type creep equation extended by a law of mixture
Multiaxial creep-fatigue rules
International Nuclear Information System (INIS)
Spindler, M.W.; Hales, R.; Ainsworth, R.A.
1997-01-01
Within the UK, a comprehensive procedure, called R5, is used to assess the high temperature response of structures. One part of R5 deals with creep-fatigue initiation, and in this paper we describe developments in this part of R5 to cover multiaxial stress states. To assess creep-fatigue, damage is written as the linear sum of fatigue and creep components. Fatigue is assessed using Miner's law with the total endurance split into initiation and growth cycles. Initiation is assessed by entering the curve of initiation cycles vs strain range using a Tresca equivalent strain range. Growth is assessed by entering the curve of growth cycles vs strain range using a Rankine equivalent strain range. The number of allowable cycles is obtained by summing the initiation and growth cycles. In this way the problem of defining an equivalent strain range applicable over a range of endurance is avoided. Creep damage is calculated using ductility exhaustion methods. In this paper we address two aspects; first, the nature of stress relaxation and, hence, accumulated creep strain in multiaxial stress fields; secondly, the effect of multiaxial stress on creep ductility. The effect of multiaxial stress state on creep ductility has been examined using experimental data and mechanistic models. Good agreement is demonstrated between an empirical description of test data and a cavity growth model, provided a simple nucleation criterion is included. A simple scaling factor is applied to uniaxial creep ductility, defined as a function of stress state. The factor is independent of the cavity growth mechanisms and yields a value of equivalent strain which can be conveniently used in determining creep damage by ductility exhaustion. (author). 14 refs, 4 figs
Revisiting Creeping Competences in the EU
DEFF Research Database (Denmark)
Citi, Manuele
2014-01-01
case where secondary legislation was employed to extend a formal treaty-based competence (civilian research and technology policy) to an area that, for historical and strategic reasons, has always been a policy monopoly of national governments: research and technology development policy for security...... and defence. Through the analysis of a large pool of documentary data, I elaborate a set of linked hypotheses about the empirical dynamics of creeping competences, and show how the theory of incomplete contracting is best suited to explain this phenomenon....
Gradual failure of structures in creep conditions
International Nuclear Information System (INIS)
Chrzanowski, M.; Latus, P.
1993-01-01
The most characteristic feature of progressive material deterioration in creep conditions Is its time-dependence. In structures this process comprises of three stages: 1. Incubation of a macroscopic defect at the time of First Crack Appearance (FCA); 2. Propagation of a macro-crack throughout the structural member at the Time of Member Failure (TMF); 3. Propagation of failure of consecutive structure members, leading to the Final Structure Collapse (FSC). The importance of a full analysis of a structure which comprises all above stages has been demonstrated previously. Corresponding times are denoted as t 1 , t 2 , t 3 respectively. Depending on many factors, like material properties, loading and supports, the ratio of t 1 /t 2 and t 2 /t 3 may vary significantly, and thus exhibiting a safety margin connected with damage propagation throughout the structure. However, the full analysis becomes very sophisticated since creep and damage evolutions law are often nonlinear ones, and analysis should include changing geometry of a structure. It was was found that the failure propagation in analysed structures appeared to be very sensitive to structures geometry and loading. The time ratio t 1 /t 3 depends on redundancy k (higher the redundancy lower the ratio), but structures collapse by local mechanisms. These mechanisms can be different depending on k. More decisive than redundancy is an overall configuration of loads and structure geometry because of different mechanism of final failure. So far, no general conclusion can be drawn, but the whole analysis resembles that of limit analysis for structures made of ideally plastic or elastic-plastic materials. Nevertheless it Is evident that full analysis of structures in creep conditions can significantly enhance the structures life-time expectation
Directory of Open Access Journals (Sweden)
Edward A. Startsev
2003-08-01
Full Text Available In plasmas with strongly anisotropic distribution functions (T_{∥b}/T_{⊥b}≪1 a Harris-like collective instability may develop if there is sufficient coupling between the transverse and longitudinal degrees of freedom. Such anisotropies develop naturally in accelerators and may lead to a deterioration of beam quality. This paper extends previous numerical studies [E. A. Startsev, R. C. Davidson, and H. Qin, Phys. Plasmas 9, 3138 (2002] of the stability properties of intense non-neutral charged particle beams with large temperature anisotropy (T_{⊥b}≫T_{∥b} to allow for nonaxisymmetric perturbations with ∂/∂θ≠0. The most unstable modes are identified, and their eigenfrequencies, radial mode structure, and nonlinear dynamics are determined. The simulation results clearly show that moderately intense beams with s_{b}=ω[over ^]_{pb}^{2}/2γ_{b}^{2}ω_{β⊥}^{2}≳0.5 are linearly unstable to short-wavelength perturbations with k_{z}^{2}r_{b}^{2}≳1, provided the ratio of longitudinal and transverse temperatures is smaller than some threshold value. Here, ω[over ^]_{pb}^{2}=4πn[over ^]_{b}e_{b}^{2}/γ_{b}m_{b} is the relativistic plasma frequency squared, and ω_{β⊥} is the betatron frequency associated with the applied smooth-focusing field. A theoretical model is developed based on the Vlasov-Maxwell equations which describes the essential features of the linear stages of instability. Both the simulations and the analytical theory predict that the dipole mode (azimuthal mode number m=1 is the most unstable mode. In the nonlinear stage, tails develop in the longitudinal momentum distribution function, and the kinetic instability saturates due to resonant wave-particle interactions.
Energy Technology Data Exchange (ETDEWEB)
Routbort, J. L.; Goretta, K. C.; Arellano-Lopez, A. R.
2000-04-27
High-temperature creep measurements combined with microstructural investigations can be used to elucidate deformation mechanisms that can be related to the diffusion kinetics and defect chemistry of the minority species. This paper will review the theoretical basis for this correlation and illustrate it with examples from some important electronic ceramics having a perovskite structure. Recent results on BaTiO{sub 3}, (La{sub 1{minus}x}Sr){sub 1{minus}y}MnO{sub 3+{delta}}, YBa{sub 2}Cu{sub 3}O{sub x}, Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub x}, (Bi,Pb){sub 2}Sr{sub 2}Ca{sub 2}Cu{sub 3}O{sub x} and Sr(Fe,Co){sub 1.5}O{sub x} will be presented.
International Nuclear Information System (INIS)
Berman, V.G.; Mishurov, Yu.N.
1980-01-01
Gas flow and its density distribution in the Galaxy spiral arm gravitational potential is calculated by means of the nonlinear theory. Line profile of H I emission in 21 cm based on the Galaxy spiral structure models proposed by Lin and Marochnik are constructed for the galactic coordinates 30 deg < or approximately |l| < or approximately 60 deg. It is shown that the conclusion about the possibility of agreement of the Marochnik model with observations made by means of the linear theory is confirmed in the nonlinear theory. In the Marochnik model distributions with R H II regions, CO-clouds, γ-radiation, supernova remnants and so on may also be understood connecting them with variation of gas compression in galactic shock with H radius
Creep behaviour of thin walled composite tubes
International Nuclear Information System (INIS)
Thiebaud, F.; Muzic, B.; Perreux, D.; Varchon, D.; Oytana, C.; Lebras, J.
1993-01-01
Fiber reinforced composites are more and more employed in high performance structure for nuclear power plant, mainly as water piping tubes. The increase of the use of composites is due to the advantages that they give : high stiffness, large ultimate strength, corrosion resistance. This last advantage is sought for the pieces in contact with water, and it's one of the reason why the composite can be preferred to metal. However the mechanical behaviour of composite is actually poorly known. The high anisotropy is the main difficulty to obtain a realistic model of behaviour. This problem implies that the safety factor used in the design of structure is often too large. In this article a general overview of the mechanical behaviour of tube made in glass epoxy material is proposed. We discuss especially the creep behaviour under biaxial loadings. The form of the proposed model presently allows predicting a nonlinearity of the behaviour and provides a good correlation with the experimental data of several tests not described in this paper. It accounts for the change of the Poisson ratio during creep and cyclic tests. However the complete identification requires long time testings and consequently the model must be corrected to take into account the damage which occurs in these cases
Numerical description of creep of highly creep resistant alloys
International Nuclear Information System (INIS)
Preussler, T.
1991-01-01
Fatigue tests have been performed with a series of highly creep resistant materials for gas turbines and related applications for gaining better creep data up to long-term behaviour. The investigations were performed with selected individual materials in the area of the main applications down to strains and stresses relevant to design, and have attained trial durations of 25000 to 60000 h. In continuing former research, creep equations for a selection of characterizing individual materials have been improved and partly newly developed on the basis of a differentiated evaluation. Concerning the single materials, there are: one melt each of the materials IN-738 LC, IN-939, IN-100, FSX-414 and Inconel 617. The applied differentiated evaluation is based on the elastoplastical behaviour from the hot-drawing test, the creep behaviour from the non interrupted or the interrupted fatigue test, and the contraction behaviour from the annealing test. The creep equations developed describe the high temperature deformation behaviour taking into account primary, secondary and partly the tertiary creep dependent of temperature, stress and time. These equations are valid for the whole application area of the respective material. (orig./MM) [de
Basko, D M
2014-02-01
We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.
Creep strain accumulation in a typical LMFBR piperun
International Nuclear Information System (INIS)
Johnstone, T.L.
1975-01-01
The analysis described allows the strain concentrations in typical LMFBR two anchor point uniplanar piperuns to be calculated. Account is taken of the effect of pipe elbows in attracting creep strain to themselves as well as possible movements of the thrust line due to strain redistribution. The influence of the initial load conditions is also examined. The stress relaxation analysis is facilitated by making the assumption that a cross-sectional stress distribution determined by the asymptotic fully developed state of creep exists at all times. Use is then made of Hoff(s) analogy between materials with a creep law of the Norton type and those with a corresponding non-linear elastic stress strain law, to determine complementary strain energy rates for straight pipes and bends. Ovalisation of the latter produces an increased strain energy rate which can be simply calculated by comparison with an equal length of straight pipe through employing a creep flexibility factor due to Spence. Deflection rates at any location in the pipework can then be evaluated in terms of the thermal restraint forces at that location by an application of Castigliano's principle. In particular for an anchor point the deflection rates are identically zero and this leads to the generation of 3 simultaneous differential equations determining the relaxation of the anchor reactions. Indicative results are presented for the continuous relaxation at 570 deg C of the thermally induced stress in a planar approximation to a typical LMFBR pipe run chosen to have peak elbow stresses close to the code maximum. The results indicate a ratio, after 10 5 hours, of 3 for creep strain concentration relative to initial peak strain (calculated on the assumption of fully elastic behavior) in the most severely affected elbow, when either austenitic 316 or 321 creep properties are employed
Directory of Open Access Journals (Sweden)
Shahriar Dastjerdi
2016-06-01
Full Text Available Nonlinear bending analysis of orthotropic annular/circular graphene sheets has been studied based on the non-local elasticity theory. The first order shear deformation theory (FSDT is applied in combination with the nonlinear Von-Karman strain field. The obtained differential equations are solved by using two methods, first the differential quadrature method (DQM and a new semi-analytical polynomial method (SAPM which is innovated by the authors. Applying the DQM or SAPM, the differential equations are transformed to nonlinear algebraic equations system. Then the Newton–Raphson iterative scheme is used. First, the obtained results from DQM and SAPM are compared and it is concluded that although the SAPM’s formulation is considerably simpler than DQM, however, the SAPM’s results are so close to DQM. The results are validated with available papers. Finally, the effects of small scale parameter on the results, the comparison between local and non-local theories, and linear to nonlinear analyses are investigated.
Comparative analysis of coupled creep-damage model implementations and application
International Nuclear Information System (INIS)
Bhandari, S.; Feral, X.; Bergheau, J.M.; Mottet, G.; Dupas, P.; Nicolas, L.
1998-01-01
Creep rupture of a reactor pressure vessel in a severe accident occurs after complex load and temperature histories leading to interactions between creep deformations, stress relaxation, material damaging and plastic instability. The concepts of continuous damage introduced by Kachanov and Robotnov allow to formulate models coupling elasto-visco-plasticity and damage. However, the integration of such models in a finite element code creates some difficulties related to the strong non-linearity of the constitutive equations. It was feared that different methods of implementation of such a model might lead to different results which, consequently, might limit the application and usefulness of such a model. The Commissariat a l'Energie Atomique (CEA), Electricite de France (EDF) and Framasoft (FRA) have worked out numerical solutions to implement such a model in respectively CASTEM 2000, ASTER and SYSTUS codes. A ''benchmark'' was set up, chosen on the basis of a cylinder studied in the programme ''RUPTHER''. The aim of this paper is not to enter into the numerical details of the implementation of the model, but to present the results of the comparative study made using the three codes mentioned above, on a case of engineering interest. The results of the coupled model will also be compared to an uncoupled model to evaluate differences one can obtain between a simple uncoupled model and a more sophisticated coupled model. The main conclusion drawn from this study is that the different numerical implementations used for the coupled damage-visco-plasticity model give quite consistent results. The numerical difficulty inherent to the integration of the strongly non-linear constitutive equations have been resolved using Runge-Kutta or mid-point rule. The usefulness of the coupled model comes from the fact the uncoupled model leads to too conservative results, at least in the example treated and in particular for the uncoupled analysis under the hypothesis of the small
Creep curve modeling of hastelloy-X alloy by using the theta projection method
International Nuclear Information System (INIS)
Woo Gon, Kim; Woo-Seog, Ryu; Jong-Hwa, Chang; Song-Nan, Yin
2007-01-01
To model the creep curves of the Hastelloy-X alloy which is being considered as a candidate material for the VHTR (Very High Temperature gas-cooled Reactor) components, full creep curves were obtained by constant-load creep tests for different stress levels at 950 C degrees. Using the experimental creep data, the creep curves were modeled by applying the Theta projection method. A number of computing processes of a nonlinear least square fitting (NLSF) analysis was carried out to establish the suitably of the four Theta parameters. The results showed that the Θ 1 and Θ 2 parameters could not be optimized well with a large error during the fitting of the full creep curves. On the other hand, the Θ 3 and Θ 4 parameters were optimized well without an error. For this result, to find a suitable cutoff strain criterion, the NLSF analysis was performed with various cutoff strains for all the creep curves. An optimum cutoff strain range for defining the four Theta parameters accurately was found to be a 3% cutoff strain. At the 3% cutoff strain, the predicted curves coincided well with the experimental ones. The variation of the four Theta parameters as the function of a stress showed a good linearity, and the creep curves were modeled well for the low stress levels. Predicted minimum creep rate showed a good agreement with the experimental data. Also, for a design usage of the Hastelloy-X alloy, the plot of the log stress versus log the time to a 1% strain was predicted, and the creep rate curves with time and a cutoff strain at 950 C degrees were constructed numerically for a wide rang of stresses by using the Theta projection method. (authors)
Prediction of long-term creep curves
International Nuclear Information System (INIS)
Oikawa, Hiroshi; Maruyama, Kouichi
1992-01-01
This paper aims at discussing how to predict long-term irradiation enhanced creep properties from short-term tests. The predictive method based on the θ concept was examined by using creep data of ferritic steels. The method was successful in predicting creep curves including the tertiary creep stage as well as rupture lifetimes. Some material constants involved in the method are insensitive to the irradiation environment, and their values obtained in thermal creep are applicable to irradiation enhanced creep. The creep mechanisms of most engineering materials definitely change at the athermal yield stress in the non-creep regime. One should be aware that short-term tests must be carried out at stresses lower than the athermal yield stress in order to predict the creep behavior of structural components correctly. (orig.)
Geometric nonlinear analysis of self-anchored cable-stayed suspension bridges.
Hui-Li, Wang; Yan-Bin, Tan; Si-Feng, Qin; Zhe, Zhang
2013-01-01
Geometric nonlinearity of self-anchored cable-stayed suspension bridges is studied in this paper. The repercussion of shrinkage and creep of concrete, rise-to-span ratio, and girder camber on the system is discussed. A self-anchored cable-stayed suspension bridge with a main span of 800 m is analyzed with linear theory, second-order theory, and nonlinear theory, respectively. In the condition of various rise-to-span ratios and girder cambers, the moments and displacements of both the girder and the pylon under live load are acquired. Based on the results it is derived that the second-order theory can be adopted to analyze a self-anchored cable-stayed suspension bridge with a main span of 800 m, and the error is less than 6%. The shrinkage and creep of concrete impose a conspicuous impact on the structure. And it outmatches suspension bridges for system stiffness. As the rise-to-span ratio increases, the axial forces of the main cable and the girder decline. The system stiffness rises with the girder camber being employed.
Geometric Nonlinear Analysis of Self-Anchored Cable-Stayed Suspension Bridges
Directory of Open Access Journals (Sweden)
Wang Hui-Li
2013-01-01
Full Text Available Geometric nonlinearity of self-anchored cable-stayed suspension bridges is studied in this paper. The repercussion of shrinkage and creep of concrete, rise-to-span ratio, and girder camber on the system is discussed. A self-anchored cable-stayed suspension bridge with a main span of 800 m is analyzed with linear theory, second-order theory, and nonlinear theory, respectively. In the condition of various rise-to-span ratios and girder cambers, the moments and displacements of both the girder and the pylon under live load are acquired. Based on the results it is derived that the second-order theory can be adopted to analyze a self-anchored cable-stayed suspension bridge with a main span of 800 m, and the error is less than 6%. The shrinkage and creep of concrete impose a conspicuous impact on the structure. And it outmatches suspension bridges for system stiffness. As the rise-to-span ratio increases, the axial forces of the main cable and the girder decline. The system stiffness rises with the girder camber being employed.
DEFF Research Database (Denmark)
Enemark, Søren; Santos, Ilmar F.
2016-01-01
In this work, the nonlinear dynamic behaviour of a vertical rigid rotor interacting with a flexible foundation by means of two passive magnetic bearings is quantified and evaluated. The quantification is based on theoretical and experimental investigation of the non-uniformity (anisotropy......) of the magnetic field and the weak nonlinearity of the magnetic forces. Through mathematical modelling the nonlinear equations of motion are established for describing the shaft and bearing housing lateral dynamics coupled via the nonlinear and non-uniform magnetic forces. The equations of motion are solved...
Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong
2015-01-01
This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.
Energy Technology Data Exchange (ETDEWEB)
Braffort, P; Chaigne, M [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1958-07-01
1) Introduction: The difficulties of the formulation of the equations of phenomena occurring during the operation of a fusion reactor are underlined. 2) The possibilities presented by analog computation of the solution of nonlinear differential equations are enumerated. The accuracy and limitations of this method are discussed. 3) The analog solution in the stationary problem of the measurement of the discharge confinement is given and comparison with experimental results. 4) The analog solution of the dynamic problem of the evolution of the discharge current in a simple case is given and it is compared with experimental data. 5) The analog solution of the motion of an isolated ion in the electromagnetic field is given. A spatial field simulator used for this problem (bidimensional problem) is described. 6) The analog solution of the preceding problem for a tridimensional case for particular geometrical configurations using simultaneously 2 field simulators is given. 7) A method of computation derived from Monte Carlo method for the study of dynamic of plasma is described. 8) Conclusion: the essential differences between the analog computation of fission reactors and fusion reactors are analysed. In particular the theory of control of a fusion reactor as described by SCHULTZ is discussed and the results of linearized formulations are compared with those of nonlinear simulation. (author)Fren. [French] 1) Introduction. On souligne les difficultes que presente la mise en equation des phenomenes mis en jeu lors du fonctionnement d'un reacteur a fusion. On selectionne un certain nombre d'equations generalement utilisees et on montre les impossibilites analytiques auxquelles on se heurte alors. 2) On rappelle les possibilites du calcul analogique pour la resolution des systemes differentiels non lineaires et on indique la precision de la methode ainsi que ses limitations. 3) On decrit esolution analogique du probleme statique de la mesure du confinement de la decharge
Precipitate Contribution to the Acoustic Nonlinearity in Nickel-Based Superalloy
Institute of Scientific and Technical Information of China (English)
Chung-Seok KIM; Cliff J.LISSENDEN
2009-01-01
The influence of γ' precipitate on the acoustic nonlinearity is investigated for a nickel-based superalloy,which is subjected to creep deformation.During creep deformation,the cuboidal γ' precipitate is preferentially coarsened in a direction perpendicular to the applied stress axis.The length and shape factor of the γ' precipitate increase with creep time.The increase of relative acoustic nonlinearity with increasing fraction of creep life is discussed in relation to the rafting of γ' precipitate,which is closely related to the scattering and distortion of the acoustic wave.
Datalogger for the creep laboratory
International Nuclear Information System (INIS)
Sambasivan, S.I.; Karthikeyan, T.V.; Chowdhary, D.M.; Anantharaman, P.N.
1989-01-01
The creep laboratory, MDL/ICGAR is a facility to study the creep properties of materials which are of interest to the fast reactor programme. The creep test is conducted over a few days to several months and years depending on the test variables employed. In these tests the creep strain and creep rate as a function of time are studied while the load and temperature are kept constant. The datalogger automates the process of recording the strain information as a function of time and also monitors the temperature throughout the test. The system handles 126 temperature channels and 42 strain channels from 27 machines. The temperature inputs are from the thermocouples and for cold junction compensation RTD's are used. An extensometer with a linear variable differential transformer (LVDT) or Super Linear Variable Capacitor (SLVC) form the set up to measure strain. The data logger consists of a front end analog input sub-system (AISS), a 8085 based Data Acquisition System (DAS) communicating to a microcomputer with CP/M operating system. The system responds to the user through the console and outputs of a dot matrix printer. The system, running a real time executive, also allows for on line enabling or disabling of a channel, printing of data, examining the current status and value, setting and getting time etc. (author)
Large earthquakes and creeping faults
Harris, Ruth A.
2017-01-01
Faults are ubiquitous throughout the Earth's crust. The majority are silent for decades to centuries, until they suddenly rupture and produce earthquakes. With a focus on shallow continental active-tectonic regions, this paper reviews a subset of faults that have a different behavior. These unusual faults slowly creep for long periods of time and produce many small earthquakes. The presence of fault creep and the related microseismicity helps illuminate faults that might not otherwise be located in fine detail, but there is also the question of how creeping faults contribute to seismic hazard. It appears that well-recorded creeping fault earthquakes of up to magnitude 6.6 that have occurred in shallow continental regions produce similar fault-surface rupture areas and similar peak ground shaking as their locked fault counterparts of the same earthquake magnitude. The behavior of much larger earthquakes on shallow creeping continental faults is less well known, because there is a dearth of comprehensive observations. Computational simulations provide an opportunity to fill the gaps in our understanding, particularly of the dynamic processes that occur during large earthquake rupture and arrest.
Creep Behaviour of Modified Mar-247 Superalloy
Directory of Open Access Journals (Sweden)
Cieśla M.
2016-06-01
Full Text Available The paper presents the results of analysis of creep behaviour in short term creep tests of cast MAR-247 nickel-based superalloy samples made using various modification techniques and heat treatment. The accelerated creep tests were performed under temperature of 982 °C and the axial stresses of σ = 150 MPa (variant I and 200 MPa (variant II. The creep behaviour was analysed based on: creep durability (creep rupture life, steady-state creep rate and morphological parameters of macro- and microstructure. It was observed that the grain size determines the creep durability in case of test conditions used in variant I, durability of coarse-grained samples was significantly higher.
Numerical integration of some new unified plasticity-creep formulations
International Nuclear Information System (INIS)
Krieg, R.D.
1977-01-01
The unified formulations seem to lead to very non-linear systems of equations which are very well behaved in some regions and very stiff in other regions where the word 'stiff' is used in the mathematical sense. Simple conventional methods of integrating incremental constitutive equations are observed to be totally inadequate. A method of numerically integrating the equations is presented. Automatic step size determination based on accuracy and stability is a necessary expense. In the region where accuracy is the limiting condition the equations can be integrated directly. A forward Euler predictor with a trapezoidal corrector is used in the paper. In the region where stability is the limiting condition, direct integration methods become inefficient and an implicit integrator which is suited to stiff equations must be used. A backward Euler method is used in the paper. It is implemented with a Picard iteration method in which a Newton method is used to predict inelastic strainrate and speed convergence in a Newton-Raphson manner. This allows an analytic expression for the Jacobian to be used, where a full Newton-Raphson would require a numerical approximation to the Jacobian. The starting procedure for the iteration is an adaptation of time independent plasticity ideas. Because of the inherent capability of the unified plasticity-creep formulations, it is felt that these theories will become accepted in the metallurgical community. Structural analysts will then be required to incorporate these formulations and must be prepared to face the difficult implementation inherent in these models. This paper is an attempt to shed some light on the difficulties and expenses involved
High temperature cracking of steels: effect of geometry on creep crack growth laws
International Nuclear Information System (INIS)
Kabiri, M.R.
2003-12-01
This study was performed at Centre des Materiaux de l'Ecole des Mines de Paris. It deals with identification and transferability of high temperature creep cracking laws of steels. A global approach, based on C * and J non-linear fracture mechanics parameters has been used to characterize creep crack initiation and propagation. The studied materials are: the ferritic steels 1Cr-1Mo-1/4V (hot and cold parts working at 540 and 250 C) used in the thermal power stations and the austenitic stainless steel 316 L(N) used in the nuclear power stations. During this thesis a data base was setting up, it regroups several tests of fatigue, creep, creep-fatigue, and relaxation. Its particularity is to contain several creep tests (27 tests), achieved at various temperatures (550 to 650 C) and using three different geometries. The relevance of the C * parameter to describe the creep crack propagation was analysed by a means of systematic study of elasto-viscoplastic stress singularities under several conditions (different stress triaxiality). It has been shown that, besides the C * parameter, a second non singular term, denoted here as Q * , is necessary to describe the local variables in the vicinity of the crack tip. Values of this constraint parameter are always negative. Consequently, application of typical creep crack growth laws linking the creep crack growth rate to the C * parameter (da/dt - C * ), will be conservative for industrial applications. Furthermore, we showed that for ferritic steels, crack incubation period is important, therefore a correlation of Ti - C * type has been kept to predict crack initiation time Ti. For the austenitic stainless steel, the relevant stage is the one of the crack propagation, so that a master curve (da/dt - C * ), using a new data analysis method, was established. Finally, the propagation of cracks has been simulated numerically using the node release technique, allowing to validate analytical expressions utilised for the experimental
Fluid Creep and Over-resuscitation.
Saffle, Jeffrey R
2016-10-01
Fluid creep is the term applied to a burn resuscitation, which requires more fluid than predicted by standard formulas. Fluid creep is common today and is linked to several serious edema-related complications. Increased fluid requirements may accompany the appropriate resuscitation of massive injuries but dangerous fluid creep is also caused by overly permissive fluid infusion and the lack of colloid supplementation. Several strategies for recognizing and treating fluid creep are presented. Copyright © 2016 Elsevier Inc. All rights reserved.
Influence of variations in creep curve on creep behavior of a high-temperature structure
International Nuclear Information System (INIS)
Hada, Kazuhiko
1986-01-01
It is one of the key issues for a high-temperature structural design guideline to evaluate the influence of variations in creep curve on the creep behavior of a high-temperature structure. In the present paper, a comparative evaluation was made to clarify such influence. Additional consideration was given to the influence of the relationship between creep rupture life and minimum creep rate, i.e., the Monkman-Grant's relationship, on the creep damage evaluation. The consideration suggested that the Monkman-Grant's relationship be taken into account in evaluating the creep damage behavior, especially the creep damage variations. However, it was clarified that the application of the creep damage evaluation rule of ASME B and P.V. Code Case N-47 to the ''standard case'' which was predicted from the average creep property would predict the creep damage on the safe side. (orig./GL)
Energy Technology Data Exchange (ETDEWEB)
Ravi, S., E-mail: sravi@igcar.gov.in; Laha, K.; Sakthy, S.; Mathew, M.D.; Jayakumar, T.
2014-02-15
Highlights: • Design of a lever type creep machine for carrying out creep test in flowing sodium. • Leveling of lever during creep was achieved by automated movement of fulcrum. • Design of creep chamber for providing constant sodium flow rate across creep specimen. • Minimum use of bellow in chamber for sodium containment and mechanical isolation. • Mini-lever mechanism to counter balance load reduction on specimen due to bellow stiffness. - Abstract: A creep testing system has been designed, fabricated, installed and validated for carrying out creep tests in flowing liquid sodium. The testing system consists of two sections namely creep testing machine and an environmental chamber. The testing system has the ability of (i) applying tensile load to the test specimen through a lever, (ii) monitoring continuously the creep elongation and (iii) allowing sodium to flow around the creep specimen at constant velocity. The annular space between the creep specimen and the environmental chamber has been suitably designed to maintain constant sodium flow velocity. Primary and secondary bellows are employed in the environmental chamber to (i) mechanically isolate the creep specimen, (ii) prevent the flowing sodium in contact with air and (iii) maintain an argon gas cover to the leaking sodium if any from primary bellow, with a provision to an alarm get activated by a spark plug. The lever-horizontality during creep test has been maintained by automatically lifting up the fulcrum instead of lowering down the pull rod as conventionally used. A mini lever mechanism has been incorporated in the load train to counter balance the load reduction on specimen from the changing stiffness of the bellows. The validation of the testing system has been established by carrying out creep tests on 316L(N) stainless steel at 873 K over a wide stress range and comparing the results with those obtained in air by employing the developed and conventional creep testing machines.
Finite element simulation for creep crack growth
International Nuclear Information System (INIS)
Miyazaki, Noriyuki; Sasaki, Toru; Nakagaki, Michihiko; Brust, F.W.
1992-01-01
A finite element method was applied to a generation phase simulation of creep crack growth. Experimental data on creep crack growth in a 1Cr-1Mo-1/4V steel compact tension specimen were numerically simulated using a node-release technique and the variations of various fracture mechanics parameters such as CTOA, J, C * and T * during creep crack growth were calculated. The path-dependencies of the integral parameters J, C * and T * were also obtained to examine whether or not they could characterize the stress field near the tip of a crack propagating under creep condition. The following conclusions were obtained from the present analysis. (1) The J integral shows strong path-dependency during creep crack growth, so that it is does not characterize creep crack growth. (2) The C * integral shows path-dependency to some extent during creep crack growth even in the case of Norton type steady state creep law. Strictly speaking, we cannot use it as a fracture mechanics parameter characterizing creep crack growth. It is, however, useful from the practical viewpoint because it correlates well the rate of creep crack growth. (3) The T * integral shows good path-independency during creep crack growth. Therefore, it is a candidate for a fracture mechanics parameter characterizing creep crack growth. (author)
A review of creep analysis and design under multi-axial stress states
International Nuclear Information System (INIS)
Yao, H.-T.; Xuan Fuzhen; Wang Zhengdong; Tu Shantung
2007-01-01
The existence of multi-axial states of stress cannot be avoided in elevated temperature components. It is essential to understand the associated failure mechanisms and to predict the lifetime in practice. Although metal creep has been studied for about 100 years, many problems are still unsolved, in particular for those involving multi-axial stresses. In this work, a state-of-the-art review of creep analysis and engineering design is carried out, with particular emphasis on the effect of multi-axial stresses. The existing theories and creep design approaches are grouped into three categories, i.e., the classical plastic theory (CPT) based approach, the cavity growth mechanism (CGM) based approach and the continuum damage mechanics (CDM) based approach. Following above arrangements, the constitutive equations and design criteria are addressed. In the end, challenges on the precise description of the multi-axial creep behavior and then improving the strength criteria in engineering design are presented
On the viscoelastic characterization of the Jeffreys-Lomnitz law of creep
Mainardi, Francesco; Spada, Giorgio
2011-01-01
In 1958 Jeffreys proposed a power law of creep, generalizing the logarithmic law earlier introduced by Lomnitz, to broaden the geophysical applications to fluid-like materials including igneous rocks. This generalized law, however, can be applied also to solid-like viscoelastic materials. We revisit the Jeffreys-Lomnitz law of creep by allowing its power law exponent $\\alpha$, usually limited to the range [0,1] to all negative values. This is consistent with the linear theory of viscoelastici...
The effects of physical aging at elevated temperatures on the viscoelastic creep on IM7/K3B
Gates, Thomas S.; Feldman, Mark
1994-01-01
Physical aging at elevated temperature of the advanced composite IM7/K3B was investigated through the use of creep compliance tests. Testing consisted of short term isothermal, creep/recovery with the creep segments performed at constant load. The matrix dominated transverse tensile and in-plane shear behavior were measured at temperatures ranging from 200 to 230 C. Through the use of time based shifting procedures, the aging shift factors, shift rates and momentary master curve parameters were found at each temperature. These material parameters were used as input to a predictive methodology, which was based upon effective time theory and linear viscoelasticity combined with classical lamination theory. Long term creep compliance test data was compared to predictions to verify the method. The model was then used to predict the long term creep behavior for several general laminates.
International Nuclear Information System (INIS)
Kim, Woo Gon; Yin, Song Nan; Kim, Yong Wan
2008-01-01
Alloy 617 is a principal candidate alloy for the high temperature gas-cooled reactor (HTGR) components, because of its high creep rupture strength coupled with its good corrosion behavior in simulated HTGR-helium and its sufficient workability. To describe a creep strain-time curve well, various constitutive equations have been proposed by Kachanov-Rabotnov, Andrade, Garofalo, Evans and Maruyama, et al.. Among them, the K-R model has been used frequently, because a secondary creep resulting from a balance between a softening and a hardening of materials and a tertiary creep resulting from an appearance and acceleration of the internal or external damage processes are adequately considered. In the case of nickel-base alloys, it has been reported that a tertiary creep at a low strain range may be generated, and this tertiary stage may govern the total creep deformation. Therefore, a creep curve for nickel-based Alloy 617 will be predicted appropriately by using the K-R model that can reflect a tertiary creep. In this paper, the long-term creep curves for Alloy 617 were predicted by using the nonlinear least square fitting (NLSF) method in the K-R model. The modified K-R model was introduced to fit the full creep curves well. The values for the λ and K parameters in the modified K-R model were obtained with stresses
Point defects and the creep of metals
International Nuclear Information System (INIS)
Nichols, F.A.
1976-01-01
Basic concepts felt to be important in diffusion-controlled creep of metals are reviewed and it is suggested that such creep is controlled by edge-dislocation climb under a rather wide range of conditions. The effect of a damage-producing flux on such creep processes is explored. It is shown that processes such as Herring-Nabarro creep are unaffected by irradiation. Evidence is presented for a climb-plus-glide mechanism of radiation creep for stresses above unirradiated yield or flow stresses. At lower stresses a preferential dislocation loop nucleation model is suggested
International Nuclear Information System (INIS)
Heard, H.C.; Durham, W.B.; Kirby, S.H.
1987-01-01
Detailed studies have been done of ice creep as related to the icy satellites, Ganymede and Callisto. Included were: (1) the flow of high-pressure water ices II, III, and V, and (2) frictional sliding of ice I sub h. Work was also begun on the study of the effects of impurities on the flow of ice. Test results are summarized
Thermal creep of Zircaloy-4 cladding
International Nuclear Information System (INIS)
Murty, K.L.; Clevinger, G.S.; Papazoglou, T.P.
1977-01-01
Data on the hoop creep characteristics of Zircaloy tubing were collected at temperatures between 600 F and 800 F, and at stress levels ranging from 10 ksi to 25 ksi using internal pressurization tests. At low driving forces, exposures as long as 2000 hours were found insufficient to establish steady state creep. The experimental data at temperatures of 650 F to 800 F correlate well with an exponential stress dependence, and the activation energy for creep was found to be in excellent agreement with that for self-diffusion. The range of stresses and temperatures is too small to study the overall effect of these variables on the activation energy for creep. The experimental steady state creep-rates and those predicted from the creep equation used agree within a factor of 1.3. These correlations imply that the mechanism for hoop creep of Zircaloy-4 cladding is characterized by an activation energy of approximately 60 kcal/mole and an activation area of about 20b 3 . In addition, the exponential stress dependence implies that the activation area for creep is stress-independent. These results suggest that the climb of edge dislocations is the rate controlling mechanism for creep of Zircaloy-4. The transient creep regime was also analysed on the premise that primary creep is directly related to the rate of dispersal of dislocation entanglements by climb. (Auth.)
Ratchetting in the creep range
International Nuclear Information System (INIS)
Ponter, A.R.S.; Cocks, A.C.F.; Clement, G.; Roche, R.; Corradi, L.; Franchi, A.
1985-01-01
This report attempts to present a ''State of the Art'' of this problem from three contracting and complementary points of view which reflect separate traditions within the discipline of structural analysis. Part I gives a brief summary of the essential elements of the three constitutive parts and a set of conclusions and recommendations are then formulated. Part II is an attempt by a group at CEA Saclay, France, to distil from available experimental data a set of rules expressed in terms of the stress classifications of the ASME codes, which will ensure the prevention of excessive creep ratchetting. The resulting stresses to an effective (or reference) stress and the creep assessment is then made in terms of the creep produced by the effective stress. They aim at analytical procedures for LMFBR components that operate in the creep region and are subject to considerable thermal transients. Part III by Ponter and Cocks of the University of Leicester is a theoretical study of the problem using bounding and other approximate techniques. The problem is studied in a sequence of increasingly complex problems commencing with an isothermal structure subjected to constant load and terminating in a structure subjected to arbitrary cyclic thermal loading. The results are expressed in terms of a reference stress derived from a plastic shakedown solution, and a reference history of temperature. These techniques are capable of providing assessment of the creep deformation of a structure when the plastic shakedown properties of the structures are known. The particular circumstances which occur in a LMFBR are emphasized. Part IV by Corradi and Franchi discusses the methods by which finite element solution may be calculated. These are surveyed with particular reference to the numerical problems involved and the relationship between computational procedure and the form of the constitutive equation. 162 refs
Stress Calculation of a TRISO Coated Particle Fuel by Using a Poisson's Ratio in Creep Condition
International Nuclear Information System (INIS)
Cho, Moon-Sung; Kim, Y. M.; Lee, Y. W.; Jeong, K. C.; Kim, Y. K.; Oh, S. C.; Kim, W. K.
2007-01-01
KAERI, which has been carrying out the Korean VHTR (Very High Temperature modular gas cooled Reactor) project since 2004, has been developing a performance analysis code for the TRISO coated particle fuel named COPA (COated Particle fuel Analysis). COPA predicts temperatures, stresses, a fission gas release and failure probabilities of a coated particle fuel in normal operating conditions. KAERI, on the other hand, is developing an ABAQUS based finite element(FE) model to cover the non-linear behaviors of a coated particle fuel such as cracking or debonding of the TRISO coating layers. Using the ABAQUS based FE model, verification calculations were carried out for the IAEA CRP-6 benchmark problems involving creep, swelling, and pressure. However, in this model the Poisson's ratio for elastic solution was used for creep strain calculation. In this study, an improvement is made for the ABAQUS based finite element model by using the Poisson's ratio in creep condition for the calculation of the creep strain rate. As a direct input of the coefficient in a creep condition is impossible, a user subroutine for the ABAQUS solution is prepared in FORTRAN for use in the calculations of the creep strain of the coating layers in the radial and hoop directions of the spherical fuel. This paper shows the calculation results of a TRISO coated particle fuel subject to an irradiation condition assumed as in the Miller's publication in comparison with the results obtained from the old FE model used in the CRP-6 benchmark calculations
Low stress creep of stainless steel
International Nuclear Information System (INIS)
Crossland, I.G.; Clay, B.D.; Baker, C.
1976-06-01
The creep of 20%Cr, 25%Ni, Nb stainless steel has been examined at temperatures from 675 to 775 0 C at sheer stressed below 13 MPa and grain sizes from 6 to 20μm. The results have indicated that the initial creep rates were linearly dependent upon stress but with a threshold stress below which no creep occurred, i.e. Bingham behaviour; in addition, the creep activation energy at small strains was substantially lower than the lattice self-diffusion value and the initial creep rates were approximately related to the grain size through an inverse cube relation. It has been concluded that at low strains (approaching the initial elastic deflection) the creep mechanism was probably that of grain boundary diffusion creep (Coble, 1963) and this is further supported by the close agreement between the observed and theoretically predicted creep rate values. Steady-state creep rates were not observed; initially the creep rates fell rapidly with strain after which a more gradual decrease occurred. Whilst the creep rate - stress relationship continued to be of a Bingham form, the progressive reduction in creep rate with strain was found to be mainly attributable to an increase in the effective viscosity, threshold stress effects being generally of secondary importance. A model has been proposed which explains the initial creep rates as being due to Cable creep with elastic accommodation at grain boundary particles. At higher strains grain boundary collapse caused by vacancy sinking is accommodated at precipitate particles by plastic deformation of the adjacent matrix material. (author)
A dissolution-precipitation mechanism is at the origin of concrete creep in moist environments
Energy Technology Data Exchange (ETDEWEB)
Pignatelli, Isabella [Laboratory for the Chemistry of Construction Materials (LC2), Department of Civil and Environmental Engineering, University of California, Los Angeles, California 90095 (United States); Kumar, Aditya [Materials Science and Engineering Department, Missouri University of Science and Technology, Rolla, Missouri 65409 (United States); Alizadeh, Rouhollah [Giatec Scientific, Ottawa, Ontario K2H 9C4 (Canada); Le Pape, Yann [Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States); Bauchy, Mathieu, E-mail: bauchy@ucla.edu, E-mail: gsant@ucla.edu [Physics of AmoRphous and Inorganic Solids Laboratory (PARISlab), Department of Civil and Environmental Engineering, University of California, Los Angeles, California 90095 (United States); Sant, Gaurav, E-mail: bauchy@ucla.edu, E-mail: gsant@ucla.edu [Laboratory for the Chemistry of Construction Materials (LC2), Department of Civil and Environmental Engineering, University of California, Los Angeles, California 90095 (United States); California Nanosystems Institute (CNSI), University of California, Los Angeles, California 90095 (United States)
2016-08-07
Long-term creep (i.e., deformation under sustained load) is a significant material response that needs to be accounted for in concrete structural design. However, the nature and origin of concrete creep remain poorly understood and controversial. Here, we propose that concrete creep at relative humidity ≥ 50%, but fixed moisture content (i.e., basic creep), arises from a dissolution-precipitation mechanism, active at nanoscale grain contacts, as has been extensively observed in a geological context, e.g., when rocks are exposed to sustained loads, in liquid-bearing environments. Based on micro-indentation and vertical scanning interferometry data and molecular dynamics simulations carried out on calcium–silicate–hydrate (C–S–H), the major binding phase in concrete, of different compositions, we show that creep rates are correlated with dissolution rates—an observation which suggests a dissolution-precipitation mechanism as being at the origin of concrete creep. C–S–H compositions featuring high resistance to dissolution, and, hence, creep are identified. Analyses of the atomic networks of such C–S–H compositions using topological constraint theory indicate that these compositions present limited relaxation modes on account of their optimally connected (i.e., constrained) atomic networks.